1R Physics Ch 5 Projectile Motion TEST Mr. Lundquist Oct 3 2014
Example of vector quantity
Acceleration
At what point in its path is the HORIZONTAL COMPONENT OF THE VELOCITY (VX) of a projectile the smallest? a. The instant it is thrown. b. Halfway to the top. c. At the top. d. As it nears the top. e. It is the same throughout the path.
Answer: E As a projectile rises towards its peak, its HORIZONTAL VELOCITY REMAINS CONSTANT while its vertical velocity decreases. This is to say that the acceleration of the object is vertical, not horizontal. Having a constant horizontal velocity, there is no point along the trajectory where the vx value is smaller than at other points.
Projectile
Any object that moves through the air or space, acted on only by gravity (and air resistance if any).
The VERTICAL ACCELERATION of a projectile is 0 m/s/s when it is at the peak of its trajectory.
FALSE - No! No! No! The vertical VELOCITY (not acceleration) 0 m/s at the peak THE VERTICAL ACCELERATION IS -9.8 M/S/S THROUGHOUT THE ENTIRE TRAJECTORY.
What is the vertical component of a projectiles path called?
Height
An object is launched at some angle, in the first second it travels 75 m horizontally. How far horizontally will it travel in the next second?
In the horizontal direction its speed does not change, so the object will travel the same distance every second.
Find the maximum and minimum ground speed for a plane traveling at 450 km/h if there is a wind of 75 km/h
Maximum 525 km/h Minimum 375 km/h
At the instant a ball is thrown horizontally with a large force, an identical ball is dropped from the same height. which ball hits the ground first?
Neither - they both hit the ground AT THE SAME TIME.
Is a cannonball rolling down a slope a projectile?
No.
The horizontal displacement (range) of a projectile is dependent upon THE TIME OF FLIGHT AND THE INITIAL HORIZONTAL VELOCITY.
TRUE - The horizontal displacement (x) can be calculated with the formula x = vox • t, where vox is the initial horizontal velocity and t is the time. These are the two variables which effect the horizontal displacement of a projectile. Memory tip - always think "range" when you read "Horizontal Component"
A projectile is a free-falling object.
TRUE - Free-falling objects, like projectiles, ARE OBJECTS UPON WHICH THE ONLY SIGNIFICANT FORCE IS GRAVITY.
A projectile could begin its projectile motion with a downward velocity.
TRUE - There is no rule about which direction a projectile must be moving at the instant it is projected. It could begin its motion with a initial downward velocity.
Describe the downward motion of a horizontally launched projectile.
The downward motion of a horizontally launched projectile is the same as that of free fall.
Define acceleration
The rate at which velocity changes
A projectile in air is subject to air resistance.
True
An airplane flies in the same direction as the wind. Is the following sentence true or false? The velocity of the airplane is the sum of the airplane's velocity relative to the air and the wind's velocity relative to the ground.
True
In the absence of air friction, the horizontal component (RANGE) of a projectile's velocity doesn't change as the projectile moves.
True
Is the following sentence true or false? A tailwind increases the velocity of an airplane.
True
Is the following sentence true or false? AT THE BEGINNING of a projectile's trajectory, the magnitude of the VERTICAL COMPONENT of the velocity IS GREATER THAN the magnitude of the HORIZONTAL COMPONENT of the velocity.
True
Is this sentence true or false? For a projectile, the horizontal component (range) of its motion is like the horizontal motion of a ball freely rolling on a level surface without friction.
True
When a projectile is thrown or launched in a horizontal (x) direction, motion follows a parabolic path
True
A cannonball shot from a cannon, a stone thrown into the air, a ball rolling off the edge of a table, a spacecraft circling Earth—all of these are examples of projectiles.
True.
An object dropped from a given height (y) will hit the ground at the same time as an object thrown horizontally, no matter how fast it is thrown (ignoring air resistance).
True.
Components of Vectors - vectors can be broken into x and y component vectors. The resultant can be found graphically or by the Pythagorean theory
True.
For the component vectors of the cannonball's motion, the horizontal component is always the same and only the vertical component changes.
True.
Is the following sentence true or false? The distance a projectile falls below its imaginary straight-line path (in the absence of gravity) is equal to the distance a freely falling object would travel in the same amount of time.
True.
Is the following sentence true or false? The length of the diagonal of a square is always 1.414 times the length of either side.
True.
Is the following sentence true or false? The two components of a vector are independent of each other.
True.
Is the following sentence true or false? Component vectors are always at right angles to each other.
True.
Is the following statement true or false? Ignoring air resistance, the horizontal component of velocity of a horizontally launched projectile remains constant.
True.
The vertical component of a projectile's velocity is like the motion for a freely falling object.
True.
Maximum range is attained when the ball is batted at an angle of nearly 45°.
True. Know this one.
Components of a vector
Two vectors at right angles that add up to a given vector.
At what angle will a thrown object travel the farthest?
Usually, the maximum range will be at an angle of 45 degrees.
The ___________ component of velocity for a projectile always changes with time.
Vertical
How fast does an object need to be moving horizontally to hit an object 50 meters away if it is thrown from the roof of a 30 meter tall building?
Vo = ? Vf a = 10 d=50 t X direction d = v t 50= v (2.45) v =20.41 m/s Vo = 0 Vf a = 10 d = 30 t Y direction d = ½ a t2 30 = ½ 10 t2 30= 5 t2 t2 = 6 t = 2.45sec
What is the horizontal distance an object moves if it is dropped from a plane moving 200 km/h and the object lands 5 seconds after it is dropped?
X direction vo vf a d t 0.055km/s 0 ? 5sec D = v×t =0.055 × 5 = 0.28 km
Circle the letter of the vertical component of velocity for the projectile launched into the air at THE PEAK of its trajectory. a. zero b. positive c. negative d. increasing
a. zero
How fast an object freely falls
v=gt v is velocity, g is acceleration, t is time
A projectile launched horizontally hits the ground in 0.8 seconds. If it had been launched with A MUCH HIGHER SPEED in the same direction, it would have hit the ground in....
0.8 seconds Gravity affects it the same. Remember the horizontal and vertical components are independent of each other. Gravity will do what it always does - no matter what. Memory tip - always think "height" when you read "Vertical Component" Memory tip - always think "range" when you read "Horizontal Component"
A ball is thrown straight upward at 10 m/s. Ideally, the ball will return to the thrower's hand with a speed of
10 m/s
What is the acceleration of an object in free fall?
10 m/s^2
In the absence of air resistance, at what other angle will a thrown ball GO THE SAME DISTANCE as one thrown at an angle of 75 degrees
15 degrees 90 - 75 = 15
A cannonball is launched from the ground at an angle of 30 degrees above the horizontal and at A SPEED OF 30 M/S. ideally the ball will land on the ground with a speed of...
30 m/s It should start and end with the SAME SPEED.
In the absence of air resistance, THE ANGLE at which a thrown ball WILL GO THE FARTHEST IS
45 degrees Know this one!
What is the ground speed of a plane with a 400 km/hr speed and a tail wind of 50 km/hr? What is the wind was a head wind?
450 km/h (tailwind), 350 km/h (headwind)
A cannonball is fired at some angle into the air. In the first second it moves 5 METERS HORIZONTALLY. Assuming it doesn't hit the ground and air resistance is negligible, HOW FAR DOES IT MOVE HORIZONTALLY in the next second?
5 meters Remember, the horizontal velocity is CONSTANT
A baseball is hurled into the air at an angle of 30 degrees above the horizontal and lands on a target that is at the same level as that where the baseball started. The baseball will also land on the SAME TARGET if it is thrown at an angle of
60 degrees 90 - 30= 60
A cannonball is launched horizontally from a tower. If the cannon has a barrel velocity of 60 m/s, where will the cannonball be second later?
60 m downrange
A cannon WITH A BARREL VELOCITY OF 140 M/S launches a cannonball horizontally from a tower. Neglecting air resistance, how far vertically will the cannonball have fallen after 4 seconds.
80 meters.
How do you find acceleration?
Acceleration = change in velocity / time
Circle the letter of each quantity that is a vector quantity. a. velocity b. time c. acceleration d. momentum
All - except for Time. Time is not a vector quantity.
Circle the letter of each statement about a horizontally launched projectile that is true. a. Gravity acts on the projectile. b. Ignoring air resistance, horizontal motion is constant. c. The projectile accelerates downward. d. The vertical motion is the same as a freely falling object.
All are true!
A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical acceleration? Its horizontal acceleration?
Answer: Its vertical acceleration is g because the force of gravity is downward. Its horizontal acceleration is zero because no horizontal force acts on it.
A football is kicked into the air at an angle of 45 degrees with the horizontal. At the very top of the ball's path, the net force acting upon it is _______. (Neglect the effects of air resistance.) a. entirely vertical b. entirely horizontal c. both vertical and horizontal d. not enough information given to know.
Answer: A A projectile is an object upon which THE ONLY FORCE IS GRAVITY. Since no other forces act upon the object, the net force would be downward.
Numerical values and directions are stated for a variety of quantities. Which of these statements represent a vector description? Include all that apply. a. 20 meters, west b. 9.8 m/s/s c. 35 mi/hr, south d. 16 years old e. 60 minutes f. 3.5 m/s/s, south g. -3.5 m/s/s h. +20 degrees C
Answer: ACFG Expressions of vector quantities would include a magnitude (number, value, etc.) and a direction. The direction could be described as being north, south, east, west or left, right, up, down. ON OCCASION, a "+" or "-" is used to describe the direction. Since mathematical computations on calculators do not fare well with the typing of "south," a - sign is often substituted for a given direction. In the case of g, the units indicate an acceleration quantity. The "-" sign indicates a direction. One must be careful in assuming that a "+" or "-" sign is a sure sign of a quantity being a direction for other non-vector quantities can use such signs as well (as is the case in h).
Which of the following quantities are vectors? Include all that apply. distance traveled displacement average speed average velocity instantaneous velocity acceleration
Answer: BDEF Of the five kinematic quantities listed here, three of them are vectors. DISPLACEMENT, VELOCITY (BOTH AVERAGE AND INSTANTANEOUS), AND ACCELERATION all require the mention of a direction in order to fully describe the quantity.
At what point in its path is the VERTICAL COMPONENT OF THE VELOCITY (VY) of a projectile the smallest? a. The instant it is thrown. b. Halfway to the top. c. At the top. d. As it nears the top. e. It is the same throughout the path.
Answer: C As a projectile rises towards its peak, its horizontal velocity remains constant while its vertical velocity decreases. During the upward portion of its trajectory, the vy continuously decreases until it becomes 0 m/s at the peak. Thus, the vy is as small as it will ever be when it is at the peak of the trajectory.
43. A bullet is fired horizontally and hits the ground in 0.5 seconds. If it had been fired with twice the speed in the same direction, it would have hit the ground in ____. (Assume no air resistance.) a. less than 0.5 s. b. more than 0.5 s. c. 0.5 s.
Answer: C Once the bullet leaves the muzzle, it becomes a projectile (assuming no air resistance). As it falls, ITS HORIZONTAL VELOCITY REMAINS CONSTANT while its vertical velocity decreases. The force of gravity acts upon the bullet to cause its downward acceleration. The motion of the bullet in the downward direction is independent of the motion in the horizontal direction. That is to say, any alteration in a horizontal aspect of its motion will not effect the motion in the vertical direction. The time to fall vertically to the ground is not effected by the horizontal speed of the projectile. It would still take 0.5 seconds to fall to the ground from this height regardless of the horizontal speed.
Which of the following descriptions of moving objects accurately PORTRAY A PROJECTILE? List all that apply. a. an object which is moving through the air and not touching any surface b. a falling skydiver with an open parachute any object upon which air resistance is negligible c. a free-falling object d. an object upon which the only significant force is the force of gravity e. a falling feather f. a falling feather in a vacuum chamber g. a falling feather in a falling vacuum chamber.
Answer: DEGH A projectile is an object upon which THE ONLY FORCE IS GRAVITY. Air resistance MUST BE NEGLIGIBLE OR NONEXISTENT. Other forces resulting from people or things pulling or pushing, attached strings or contact with surfaces must not be present. a. NO - A plane moves through the air and is not touching any surface. Yet, a plane is clearly not a projectile. b. NO - A falling skydiver typically experiences considerable air resistance. It is popular to describe such skydivers as being in free fall. This is an erroneous use of the term. c. NO - As you sit in your chair, air resistance is negligible. You are certainly not a projectile (at least, we hope not). d. YES - A projectile is an object in free fall. e. YES - An object upon which the only significant force is gravity fits the definition of a projectile (provided that significant means "having an influence"). f. NO - Falling feathers encounter air resistance which impedes the downward acceleration and causes the feather to fall at nearly a constant velocity. g. YES - When a feather is allowed to fall in a vacuum, air resistance is eliminated and the feather can free fall. h. YES - When a feather is allowed to fall in a vacuum and the vacuum is free-falling as well, air resistance is eliminated and an observer would notice that both the vacuum chamber and the feather are in free fall.
At what point in its path does a projectile have minimum speed?
At the top of it's path or trajectory. This is because the vertical component of it's velocity is 0.
The FINAL vertical velocity of a projectile is always equal to the initial vertical velocity.
FALSE - Horizontal Velocity is constant - not vertical. A projectile launched at an angle forms a parabolic trajectory. Suppose that one were to trace a projectile's motion forward in time from the peak and backwards in time from the peak. If done, one would find that the vertical velocity value has the same magnitude for equal amounts of times traced forward and backward from the peak. So for the same time before and after the peak, a projectile has the same speed. However, some projectiles are not launched from the same height at which they land. The final height is not the same as the initial height and as such the time to rise to the peak is not equal to the time to fall from the peak. In such instances, the initial vertical velocity is not equal to the final vertical velocity.
As a projectile rises towards the peak of its trajectory, the vertical acceleration will decrease; as it falls from the peak of its trajectory, its vertical acceleration will decrease.
FALSE - This would be a true description of the vertical velocity. THE VERTICAL ACCELERATION IS A CONSTANT VALUE OF 9.8 M/S/S THROUGHOUT THE ENTIRE TRAJECTORY.
A projectile with an upward component of motion will have a upward component of acceleration.
FALSE - All projectiles experience A DOWNWARD ACCELERATION, whether they are moving upward or downward. The upward-moving projectiles have an upward velocity, but the actual velocity values are getting smaller; that is, the projectile IS SLOWING DOWN ON THE WAY TO ITS PEAK.
Vectors can be added together; scalar quantities cannot.
FALSE - BOTH VECTORS AND SCALARS CAN BE ADDED TOGETHER. The rules for adding vectors together are unique to vectors and cannot be used when adding scalars together. The direction of a vector must be considered when adding two vectors together.
As a projectile rises towards the peak of its trajectory, the vertical acceleration is directed upward; as it falls from the peak of its trajectory, its vertical acceleration is directed downward.
FALSE - Not only is the magnitude of the vertical acceleration a constant value throughout a projectile's trajectory, the direction is constant as well. PROJECTILE'S AT ALL TIMES REGARDLESS OF ANY OTHER VARIABLE WILL ACCELERATE DOWNWARDS AT 9.8 M/S/S. This is perhaps the most important truth to digest about projectiles.
The vertical component (height) of a projectile's velocity is constant.
FALSE - Projectiles are objects being acted upon by gravity. As such, there is a vertical acceleration; the vertical velocity is not constant, but changing. Memory tip - always think "height" when you read "Vertical Component"
A scalar quantity can have a direction associated with it.
FALSE - Scalars are defined as quantities which are fully described by their magnitude alone. Scalars have no regard for direction and it is MEANINGLESS to associate a direction with such a quantity.
The horizontal velocity of a projectile is 0 m/s at the peak of its trajectory.
FALSE - THE VERTICAL VELOCITY OF A PROJECTILE IS 0 M/S AT THE PEAK OF ITS TRAJECTORY; but the horizontal component of the velocity at the peak is WHATEVER THE VALUE WAS WHEN FIRST LAUNCHED.
Consider a projectile launched from ground level at a fixed launch speed and a variable angle and landing at ground level. The horizontal displacement (range) of the projectile WILL ALWAYS INCREASE as the angle of launch is increased from 0 degrees to 90 degrees.
FALSE - The range (or horizontal displacement) will increase as the angle is increased from 0 degrees to 45 degrees. THE MAXIMUM RANGE OCCURS AT 45 DEGREES. As the angle is further increased to values greater than 45 degrees, the horizontal displacement decreases. Memory tip - always think "range" when you read "Horizontal Component"
The time that a projectile is in the air is dependent upon the horizontal component (range) of the initial velocity.
FALSE - The time for a projectile to rise vertically to its peak (and subsequently fall back to the ground) is dependent upon THE INITIAL VERTICAL VELOCITY. Alteration in the horizontal velocity will only cause the projectile to have a greater horizontal displacement (x).
As a projectile rises towards the peak of its trajectory, THE HORIZONTAL VELOCITY WILL DECREASE; as it falls from the peak of its trajectory, its horizontal velocity will decrease.
FALSE - This is a true description for the vertical component (height) of the velocity. The horizontal velocity is unchanging or CONSTANT throughout the trajectory of a projectile!!!
As a projectile rises towards the peak of its trajectory, the vertical velocity will decrease; as it falls from the peak of its trajectory, its vertical velocity will decrease.
FALSE - Upward-rising projectiles have a DOWNWARD ACCELERATION; THIS MEANS THEY ARE SLOWING DOWN AS THEY RISE. Thus, The magnitude of their velocity is decreasing. Downward-moving projectiles also have a downward acceleration; THIS MEANS THEY ARE SPEEDING UP. The magnitude of their velocity is increasing.
Assume that a kicked ball in football is a projectile. If the ball takes 3 seconds to rise to the peak of its trajectory, then it will take 6 seconds to fall from the peak of its trajectory to the ground.
FALSE - Close, but very false. If it takes 3 seconds to rise to the peak, then it takes 3 seconds to fall from the peak; The 6 seconds is the total time of flight of the projectile.
A projectile cannot have a horizontal velocity.
FALSE - Many projectiles ARE MOVING FROM LEFT TO RIGHT and from right to left AS THEY SIMULTANEOUSLY FREE FALL. Such projectiles have a horizontal motion. While a projectile can have a horizontal motion, IT CANNOT HAVE A HORIZONTAL ACCELERATION. Whatever motion which it has in the horizontal dimension, must be motion with A CONSTANT HORIZONTAL VELOCITY.
A projectile must be moving IN THE DOWNWARD DIRECTION.
FALSE - Projectiles can be moving either upward or downward or at an angle to the vertical. They must however BE ACCELERATING DOWNWARD (meaning heading back to the ground), consistent with gravity's effect on an object.
The VERTICAL COMPONENT (height) of a projectile's velocity is a constant value of 9.8 m/s.
FALSE - The vertical component (height) of a projectile's velocity IS CONSTANTLY CHANGING. It is the ACCELERATION which has a value of 9.8 m/s/s. (they forgot to square it) Memory tip - always think "height" when you read "Vertical Component"
The HORIZONTAL VELOCITY of a projectile changes by 9.8 m/s each second.
FALSE - Trick question. A projectile has A CONSTANT HORIZONTAL VELOCITY. The VERTICAL VELOCITY will change by 9.8 m/s each second.
A projectile is always subject to at least two forces.
False (think of an object in free fall)
In the absence of air friction, the vertical component (HEIGHT) of a projectile's velocity doesn't change as the projectile moves
False Yes the height changes. If you throw something, it falls to the ground. The height decreases.
Is the following sentence true or false? Vectors can only be used to add velocities that are parallel to each other.
False.
Velocity is a scalar quantity
False.
How does the horizontal component of a projectile change as the projectile moves? Why is this the case?
HORIZONTAL COMPONENT OF VELOCITY DOES NOT CHANGE, REMAINS constant, because there is no force in x direction.
Define speed
How fast an object is moving
Define velocity
How fast an object is moving AND THE DIRECTION IT'S GOING
How does the speed of a projectile at the beginning of a launch compare with the speed at the end of the launch, ignoring air resistance?
If there is no air resistance, the speed of the projectile at the beginning is the same as its speed at the end of the launch.
What is the acceleration of a thrown object on the way up, at the top, and on the way down?
In all three situation the acceleration will be the same 9.8 (10) m/s2 because of the gravity.
Sketches in physics often include arrows, in which each arrow represents the ________ and the _______of a quantity.
Magnitude & direction
Can a scalar quantity be made into a vector quantity by adding a direction to its magnitude? Explain why or why not and give an example.
Not necessarily. Adding direction to a scalar quantity might result in a nonsensical quantity such as 5 gallons east or a teaspoon north. That makes no sense.
What is the horizontal component of a projectiles path called?
Range
In the spaces below, write an example of a vector quantity and a scalar quantity.
Scholar should be able to write an example of each.
Example of scalar quantity
Speed
What does the slope of the curve on a position vs. time graph represent?
Speed alone POSITION vs Time Graph then slope (m) = speed alone (no direction)
The peak height to which a projectile rises above the launch location is dependent upon the initial vertical velocity.
TRUE - The initial vertical velocity has an effect on the time taken by a projectile to rise towards its peak. It also effects the average speed of the projectile as it rises towards its peak. As a result, any alteration in the vertical velocity will alter the peak height of the projectile.
Consider a projectile launched from ground level at a fixed launch speed and a variable angle and landing at ground level. The vertical displacement (height) of the projectile during the first half of its trajectory (i.e., the peak height) will always increase AS THE ANGLE OF LAUNCH is increased from 0 degrees to 90 degrees.
TRUE - An increase in the angle of launch (from 0 to 90 degrees) will always increase the vertical component of the initial velocity (viy). This increase in viy will lead to increased times for the projectile rising towards its peak. And an increased angle causes the projectile to move with a greater average speed during its path towards its peak. Both of these effects lead to the outcome that the peak height of a projectile will increase as the angle of launch increases from 0 to 90 degrees.
Consider a projectile launched from ground level at a fixed launch angle and a variable launch speed and landing at ground level. The vertical displacement (height) of the projectile during the first half of its trajectory (i.e., the peak height) will always increase AS THE LAUNCH SPEED is increased.
TRUE - As the launch speed is increased, the components of the initial velocity (both the horizontal and the vertical) increase as well. This causes the projectile to stay in the air for a longer period of time and to be moving faster in the vertical direction. The result is that increased launch speeds always lead to increased heights for projectiles.
The vertical velocity of a projectile is 0 m/s at the peak of its trajectory.
TRUE - At the peak of its trajectory, a projectile IS IN THE PROCESS OF CHANGING DIRECTIONS. The vertical velocity must change from a positive value (+ for upward) to a negative value (- for downward). This transition means that the value for the vertical velocity must at sometime be in between a + and - number. THE IN-BETWEEN NUMBER IS 0 M/S AND THIS OCCURS AT THE PEAK.
The horizontal velocity of a projectile IS UNAFFECTED BY THE VERTICAL VELOCITY; these two components of motion are independent of each other.
TRUE - For any two dimensional motion (whether projectile motion or riverboat problems or ...), perpendicular components of the motion ARE INDEPENDENT OF EACH OTHER. Any alteration in a vertical component will not effect the horizontal components of motion. Memory tip - always think "range" when you read "Horizontal Component"
For a projectile which lands at the same height that it is projected from, the time to rise to the peak is equal to the time to fall from its peak to the original height.
TRUE - For projectiles launched at upward angles and landing at the original height, the time to the rise to the peak equals the time to fall from the peak. If it takes 3 seconds to rise upward, it will take 3 seconds to fall.
The final horizontal velocity of a projectile is always EQUAL to the initial horizontal velocity.
TRUE - Since THERE IS NO HORIZONTAL ACCELERATION FOR A PROJECTILE, the initial horizontal velocity is equal to the final horizontal velocity. HORIZONTAL VELOCITY IS CONSTANT!!!!
A projectile with an downward component of motion will have a downward component of acceleration.
TRUE - This is a true statement. It could also be said that a projectile with an upward component of motion also has a downward acceleration. ALL PROJECTILES ACCELERATE IN THE DOWNWARD DIRECTION. Period.
A vector quantity always has A DIRECTION ASSOCIATED with it.
TRUE - Vectors are defined as quantities which are fully described by both their magnitude AND DIRECTION. By definition, a vector has a direction associated with it. If it didn't, then it would NOT be a vector.
A projectile does not have to have horizontal motion.
TRUE - A projectile could be moving strictly IN A VERTICAL DIRECTION with no horizontal motion. A ball thrown straight up in the air would be such a case.
The vertical component (height) of a projectile's velocity is changing at a constant rate.
TRUE - A projectile has a vertical acceleration of 9.8 m/s/s THROUGHOUT THE ENTIRE TRAJECTORY. This acceleration value is constant. This means that the vertical velocity changes by the same amount - 9.8 m/s - during each second of its motion. There is a change in the vertical velocity by a constant amount. Memory tip - always think "height" when you read "Vertical Component"
A projectile with a horizontal component of motion will have A CONSTANT HORIZONTAL VELOCITY.
TRUE - Absolutely true! Projectiles are objects BEING ACTED UPON BY GRAVITY ALONE. As such, there is a vertical acceleration but NO HORIZONTAL ACCELERATION. REMEMBER THIS: THE HORIZONTAL VELOCITY OF A PROJECTILE IS EITHER A CONSTANT ZERO OR A CONSTANT VALUE.
The time that a projectile is in the air is dependent upon the vertical component (height) of the initial velocity.
TRUE - Absolutely true. Projectiles with a greater vertical component (height) of initial velocity will be in the air for longer amount of times (assuming that the direction of viy is upward). An alteration in the viy value will alter the time of flight of the projectile, regardless of the direction of viy.
The vertical component (height) of a projectile's velocity is changing.
TRUE - Projectiles are objects being acted upon by gravity alone. As such, there is a vertical acceleration; the vertical velocity is not constant, but changing. Memory tip - always think "height" when you read "Vertical Component"
A projectile must be ACCELERATING in the downward direction.
TRUE - The force of gravity acts directly downwards upon an object, causing a downward acceleration. Any projectile MUST BE ACCELERATING DOWNWARDS regardless of other features of its motion.
A projectile experiences negligible or no air resistance.
TRUE - The only force on a projectile is gravity; AIR RESISTANCE MUST NOT BE PRESENT or must not have an influence upon the motion of the projectile.
The magnitude of the vertical velocity of a projectile changes by 9.8 m/s each second.
TRUE - This is absolutely true .
Vectors can be represented by an arrow on a scaled diagram; the length of the arrow represents the vector's magnitude and the direction it points represents the vector's direction.
TRUE - This is exactly the case and exactly what is done throughout the unit.
A projectile needs to be "falling."
TRUE - To many, "falling" means being pulled downward by gravity's force. In this case, a projectile must be "falling" or must however BE ACCELERATING DOWNWARD (meaning heading back to the ground), consistent with gravity's effect on an object.
How does the acceleration of an object dropped compare with the acceleration of an object thrown upward at an angle?
The acceleration in both situations will be the same because of the gravity. In both situation acceleration is 9.8 (10) m/s2.
Why doesn't an object travel as far in real life as the physics equations predict it will?
The equations do not take into account the air resistance. But in reality air resistance is significant and it will affect the path of the object.
What are the components of an objects velocity at the top of its path, when the object is thrown at an angle?
The horizontal velocity is constant - it does not change. The vertical component will be zero.
What is the resultant of two perpendicular vectors?
The resultant of two perpendicular vectors is the diagonal of a rectangle constructed with the two vectors as sides.
A thrown object will travel the same distance when thrown at two different angles. If we know one of the angles, how do we find the other one?
The two angles are complementary (their sum equals to 90 degrees. Example: if one angle is 15degrees , the other angle would be 75degrees.
How does the vertical component (height) of a projectile change as the projectile moves? Why is this the case?
The vertical component (height) of the projectile will change BECAUSE OF GRAVITY.
Describe how far below an imaginary straight-line path a projectile falls.
The vertical distance a projectile falls below an imaginary straight-line path increases continually with time and is equal to 5t² meters.
How far will a projectile launched horizontally fall after one second, two seconds, three seconds, four seconds, and five seconds?
Time (sec) Distance(m) 1 5 2 20 3 45 4 80 5 125 Formula used for the vertical direction is d = ½ a t2 = ½ 10 t2 = 5 t2
A projectile is subject to the force of gravity.
True
A projectile moves through air or space.
True
The greater the launch angle, the higher the projectile will go.
True
Resultant - the vector representing the sum of multiple vectors (as in VR = V1 + V2 above)
True.
The same range is obtained for two different projection angles—angles that add up to 90°. An object thrown into the air at an angle of 60° will have the same range as at 30° with the same speed. Maximum range is usually attained at an angle of 45°.
True.
How far will an object thrown horizontally fall four seconds after it is thrown?
Vo = 0 Vf a = 10 d=? t=4sec d = ½ a t2 = ½ 10 42 = 80 m
A ball launched into the air at 45° to the horizontal initially has a. equal horizontal and vertical components. b. components that do not change in flight. c. components that affect each other throughout flight. d. a greater component of velocity than the vertical component.
a.
When no air resistance acts on a fast-moving baseball, its acceleration is a. downward, g (gravity). b. due to a combination of constant horizontal motion and accelerated downward motion. c. opposite to the force of gravity. d. at right angles.
a.
Circle the letter of each quantity that is a scalar quantity. a. 5 liters b. 10 m/s north c. 32 minutes d. 2 cm south
a. 5 liters and c. 32 minutes (no direction listed in either!)
A boy drops a rock off a cliff at the same time that his sister throws another rock horizontally from the cliff. Circle the letter of each statement about the two rocks that is true. a. Gravity acts on both rocks. b. Both rocks hit the ground at the same time. c. Both rocks accelerate horizontally and vertically. d. Both rocks follow parabolic paths.
a. Gravity acts on both rocks. b. Both rocks hit the ground at the same time.
A ball is dropped off the edge of a desk. Another ball rolls off the desk at exactly the same time. Circle the letter that best describes the vertical component (height) of velocity of the balls. a. equal b. opposite c. zero d. constant
a. equal
What is the resultant of a 10-unit and 24-unit vector at right angles to each other?
a2 + b2 =c2 102 + 242 = c2 676 = c2 26units = c
What is the speed of an object thrown horizontally at 11 m/s after 5 sec.
a2 + b2 =c2 112 + 502 = c2 121+2500 = c2 2621 = c2 51.2m/s= c
Find the resultant velocity and direction (theta θ) of a boat crossing a river if the boat has a velocity of 12 km/h and the river has a current of 5 km/h.
a2 + b2 =c2 122 + 52 = c2 169 = c2 13km/h = c
What is the resultant of a pair of 25-unit vectors at right angles to each other?
a2 + b2 =c2 252 + 252 = c2 1250 = c2 35.35 units = c
What does the slope of the curve on a velocity vs. time graph represent?
acceleration (speed with direction) VELOCITY vx Time Graph then slope (m) = acceleration
A ball thrown in the air will never go as far as physics ideally would predict because
air friction slows the ball Know this one!
What are some examples of objects that are NOT projectiles?
an airplane, a ball rolling down an incline.
What are some examples of objects that are projectiles?
an apple falling out of a tree, a cannonball thrown in the air by a launcher.
At what part of a path does a projectile have MINIMUM SPEED?
at THE TOP of its path
Without air resistance, the time for a vertically tossed ball to return to where it was thrown is: a. 10 m/s for every second in the air. b. the same as the time going upward. c. less than the time going upward. d. more than the time going upward.
b.
A diagram includes a 3-cm long arrow pointing to the right. The arrow is a vector scaled so that 1 cm = 10 m/s. Circle the letter of the statement that best describes the vector. a. 3 cm to the right b. 30 m/s to the right c. to the right d. 60 km/h to the right
b. 30 m/s to the right
What two things are required of a vector quantity? a. force and time b. direction and magnitude c. time and temperature d. direction and mass
b. Direction and Magnitude
Circle the letter that best describes the HORIZONTAL COMPONENT of velocity for a projectile. a. zero b. constant c. varying d. increasing
b. constant Gravity issue.
Circle the letter that best describes how two scalar quantities are multiplied. a. using scientific notation b. like ordinary numbers c. by taking the square root of the sum of their squares d. multiplying their magnitudes and subtracting their directions
b. like ordinary numbers
An ultra-light aircraft traveling north at 40 km/h in a 30-km/h crosswind (at right angles) has a groundspeed of a. 30 km/h. b. 40 km/h. c. 50 km/h. d. 60 km/h.
c. Use the Pythagorean Theorem
Circle the letter of the resultant of a 3-unit vector and a 4-unit vector that are perpendicular. a. 1-unit vector b. 3-unit vector c. 5-unit vector d. 7-unit vector
c. 5-unit vector Pythagorean Theorem
Circle the letter that best describes the relationship between the vertical and horizontal components of velocity for a projectile. a. equal b. opposite c. independent d. constant
c. Independent
Circle the letter that best describes the path followed by a ball that rolls off the edge of a desk. a. straight b. circular c. curved d. horizontal
c. curved
Any vector can be resolved, or broken, into an equivalent set of two ________ vectors at right angles to each other.
component
How FAR an object freely falls from REST
d=1/2g(t squared)
The equation for the distance a projectile falls below its imaginary straight-line path is ________________
d=5t(squared)meters Must know this
How far an object freely falls
d=average velocity * t
Vector - a physical quantity that has both magnitude and direction. Give some examples:
displacement, velocity, acceleration, force
Scalar - a physical quantity that has only magnitude but no direction. Give some examples:
distance, speed, time, mass
A ball is thrown into the air at some angle. At the very top of the ball's path, its velocity is
entirely horizontal
An object is dropped and falls freely to the ground with an acceleration of g. if it is thrown upward at an angle instead, its acceleration would be
g downward
The curving path followed by a projectile in air is due to ______________
gravity
A ball is thrown into the air at an angle. The velocity of the ball can be resolved into _________ and _________ components.
horizontal and vertical
Scalar quantity
includes ONLY magnitude
Vector quantity
includes magnitude and direction
A projectile is fired horizontally IN A VACUUM. The projectile maintains its horizontal component of speed because it
is not acted on by any horizontal forces. The Horizontal component stays the same. Memory tip - always think "range" when you read "Horizontal Component"
A scalar quantity includes only
magnitude.
The path of a projectile with constant horizontal motion and a downward acceleration due to gravity is a(n) _____________ .
parabola
Circle the letter that describes the motion of a ball thrown horizontally in the absence of gravity. a. diagonally downward b. vertically downward c. parabolic d. perfectly horizontal
perfectly horizontal
The result of adding two vectors is called the
resultant
After a rock that is thrown straight up. WHEN IT REACHES THE TOP OF ITS PATH and is starting to fall back down, its ACCELERATION is....
the same as when it was at the top of its path.
The horizontal component of a projectile's VELOCITY is INDEPENDENT of
the vertical component of its VELOCITY Memory tip - always think "height" when you read "Vertical Component"
The path of a projectile is also called its ___________.
trajectory
How do you find the velocity?
v = d/t
If an object is launched horizontally at a velocity of 200 m/s, how far downrange will it be 4 seconds later?
vo = 200m/s vf - a = 0 d ? t= 4sec Range is the distance in x direction d = v × t d = 200 × 4 = 800 m
