Horizontal Projectiles and Projectile Motion
If the Vx and Vy are already known, you can solve for V by...
using the: Pythagorean Theorem Tan θ = opp / adj
True or false: A projectile with a downward component of motion will have a downward component of acceleration
True
True or false: A projectile's horizontal component of motion will have a constant horizontal velocity
True
Is time a scalar?
Yes Ex: 30.0 seconds
Is velocity a vector?
Yes Ex: 5.6 m/s downward
When you are finding maximum height but do not have a full projectile, what do you have to do?
Add on the Δy at the end to create a full trajectory.
Cos θ
Adjacent / Hypotenuse
Is displacement a vector?
Yes Ex: 21 m West
True or false: 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
At what rate does vertical velocity increase?
-9.8 m/s^2
At the maximum height, the vertical component of the velocity (vy) is...
0 m/s
For an object being pushed/driven/rolled/telekinetically moved off a horizontal table, what is the value of the initial vertical velocity, Vyi?
0 m/s
What is Vy at maximum height?
0 m/s
What is the acceleration of horizontal velocity during projectile motion?
0 m/s^2
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)
0.5 seconds
If Δy = 0 m, then the time at the maximum height is...
1/2 the total time
At what angle should I kick a soccer ball to make it go the farthest horizontal distance, Δx?
45°
A projectile is launched at an angle of 15 degrees above the horizontal and lands down range. For the same speed, what other projection angle would produce the same downrange distance?
75 degrees Complimentary angles (add up to 90 degrees)
What is free fall acceleration?
A drop from rest Motion in the y/vertical direction The object moves only because of the force of gravity Causes an object to accelerate downward at a rate of 9.80 m/s^2 (or just -9.80 m/s^2)
What is a full trajectory?
A full arc of motion of a projectile Δy = 0 m Ex: a kicked football
Vectors along an axis are represented by...
Arrows
How does height affect time?
As height increases, time increases as well.
How does initial velocity affect maximum height?
As initial velocity increases, maximum height increases as well.
How does the angle of a projectile affect maximum height?
As the angle increases, the maximum height increases as well.
How does initial velocity affect range?
As the initial velocity increases, range increases as well.
How does initial velocity affect time?
As the initial velocity increases, time increases as well.
At what point in its path is the vertical component of the velocity (Vy) of a projectile the smallest?
At the top Vy = 0 m/s
Two projectiles are fired at equal speeds but different angles. One is fired at an angle of 30 degrees and the other at 60 degrees. The projectile to hit the ground first will be the one fired at... (neglect air resistance)
Both hit at the same time.
Two toy trucks roll off the same table. One truck is traveling at 2 m/s; the other at 6 m/s. Which is in the air the longest?
Both trucks will be in the air for the same amount of time because horizontal velocity does not affect the amount of time a projectile is in the air.
True or false: A projectile is a falling feather in a vacuum chamber (container with no air)
True
Is horizontal velocity constant or not constant?
Constant
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, its velocity is...
Entirely horizontal Vy = 0 m/s
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, its acceleration is...
Entirely vertical ax = 0 m/s^2 ay = -9.8 m/s^2
True or false: A projectile does not have a horizontal velocity
False
True or false: A projectile has a horizontal velocity that changes by 9.8 m/s each second
False
True or false: A projectile is a falling skydiver with an open parachute
False
True or false: A projectile must be moving in the downward direction
False
True or false: A projectile with a rightward component of motion will have a rightward component of acceleration
False
True or false: A projectile with an upward component of motion will have an upward component of acceleration
False
True or false: 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
True or false: 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
True or false: 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
True or false: Assume that a kicked ball in a football is a projectile. If the pall 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
True or false: Consider a projectile launched from ground level at a fixed launch speed and a variable angle and landing at ground level. The horizontal displacement (i.e. the range) of the projectile will always increase as the angle of launch is increased from 0 degrees to 90 degrees
False
True or false: The final vertical velocity of a projectile is always equal to the initial vertical velocity
False
True or false: The horizontal velocity of a projectile is 0 m/s at the peak of its trajectory
False
True or false: The time that a projectile is in the air is dependent upon the horizontal component of the initial velocity
False
True or false: The vertical acceleration of a projectile is 0 m/s/s when it is at the peak of its trajectory
False
True or false: The vertical component of a projectile's velocity is a constant value of 9.8 m/s
False
True or false: The vertical component of a projectile's velocity is constant
False
True or false: A projectile is a falling feather
False Ex: Air resistance
True or false: A projectile is an object which is moving through the air and not touching any surface
False Ex: airplane, bird --> not projectiles
True or false: A projectile is any object upon which air resistance is negligible
False Ex: Not enough info --> could literally be ANY object, like a rolling ball
What is -9.80 m/s^2?
Gravity
What is projectile motion?
Has motion in the vertical direction due to free fall (accelerating at -9.80 m/s^2) The only force is gravity Also has motion horizontally Ignoring air resistance, the horizontal velocity remains constant
What is time determined by?
Height
What must the initial velocity be resolved into?
Horizontal (vx) and vertical (vy) components using cosine and sine
Δx
Horizontal displacement Range
How does height affect range?
If height increases, the range increases as well.
How does height affect time?
If height increases, time increases as well.
For an object hit/thrown/kicked at an angle, how does the value of the final vertical velocity, Vyf, compare to the value of the initial vertical velocity, Vyi?
If Δy = 0 m, then the vertical and final velocities will be opposite values. Ex: 12 m/s and -12 m/s
What can you do to maximize range?
Increase angle to 45°
What two variables can we change to increase the vertical distance, Δy, an object travels during projectile motion and how do we change them?
Increase initial velocity and maximize the angle to 90°
If I want to increase how long an object is in the air during projectile motion, what value should I change and how should I change it?
Increase the angle to maximize it to 90°.
Do horizontal and vertical velocity act independently or dependently?
Independently, but they happen at the same time
How are vectors resolved into components?
Initial velocity (original vector), horizontal velocity, vertical velocity, and the angle all come together to form a triangle shape (primarily for solving problems). The base is horizontal velocity. The height is vertical velocity. The hypotenuse is the initial velocity / original vector.
At what point in its path is the horizontal component of the velocity (Vx) of a projectile the smallest?
It is the same throughout the path.
What type of relationship do horizontal velocity and range have?
Linear If horizontal velocity increases, range increases as well.
What are vectors?
Measurements that have both a magnitude and direction
What are scalars?
Measurements that only have magnitude
For full trajectory, do you use the initial velocity?
Only when using trigonometry to find the Vx and Vy
Tan θ
Opposite / Adjacent
Sin θ
Opposite / Hypotenuse
What type of relationship do height and range have?
Polynomial If height increases, range increases.
True or false: The vertical displacement could be positive, negative, or zero.
Positive: lands higher than it started Negative: lands lower than it started Zero: lands on the same level as it started
Roll a bowling ball off the edge of a table. As it falls, its horizontal component of velocity...
Remains the same
To avoid the quadratic formula when the equation is not full trajectory...
Solve for Vf and then for time
What two variables can we change to increase the horizontal distance, Δx, an object travels during projectile motion and how do we change them?
Speed and increasing the angle to 45° If we decrease these factors, Δx will decrease as well.
True or false: A projectile is a free-falling object
True
What acts upon the vertical component of velocity and what does it cause the velocity to do?
The force of gravity at -9.80 m/s^2 acts upon the vertical component of velocity and causes it to accelerate uniformly.
What is the straight path of an object that goes straight (horizontally) outward from the top of a cliff/heightened platform?
The gravity-free path When an object makes an arc as part of its projectile motion, the top part of the arc (the part above the gravity-free path) does not count as part of the displacement.
How does the final horizontal velocity, Vxf, compare to the initial horizontal velocity, Vxi, during projectile motion for any object?
The initial horizontal velocity is always the same as the final horizontal velocity.
How does the angle of a projectile affect range and time?
The range and time are maximized at 45° As the angle increases after 45°, the range decreases, but time does not. As the angle increases, time continues to increase. Angle and range have a polynomial relationship.
True or false: A projectile must be accelerating in the downward direction
True
You can find the angle of a projectile by using...
The trigonometry inverses
Two toy trucks roll off the same table. One truck is traveling at 2 m/s; the other at 6 m/s. Which will land farther from the table?
The truck traveling at 6 m/s will land farther from the table because it is moving at a faster horizontal velocity than the other truck. Horizontal velocity affects range; the faster an object's velocity, the larger range it will have.
What is the relationship between horizontal and vertical acceleration?
They are both constant.
What is the common variable between horizontal and vertical motion?
Time
How does horizontal velocity affect time?
Time is not affected by horizontal velocity.
True or false: A projectile does not have to have horizontal motion
True
True or false: A projectile does not need to be "falling"
True
True or false: A projectile experiences negligible or no air resistance
True
True or false: Consider a projectile launched from ground level at a fixed launch angle and a variable speed and landing at ground level. The horizontal displacement (i.e. the range) of the projectile will always increase as the launch speed is increased
True
True or false: Consider a projectile launched from the ground at a fixed launch speed and a variable angle and landing at ground level. The vertical displacement 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 from 90 degrees.
True
True or false: Consider a projectile launched from the ground at a fixed launch speed and a variable angle and landing at ground level. The vertical displacement 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
True or false: 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
True or false: For the same upward launch angles, projectiles will stay in the air longer if the initial velocity is increased
True
True or false: The magnitude of the vertical velocity of a projectile changes by 9.8 m/s
True
True or false: The peak height to which a projectile rises above the launch location is dependent upon the initial vertical velocity
True
True or false: The vertical component of a projectile's velocity is changing
True
True or false: The vertical component of a projectile's velocity is changing at a constant rate
True
True or false: The vertical velocity of a projectile is 0 m/s at the peak of its trajectory
True
True or false: The vertical velocity of a projectile is unaffected by the horizontal velocity; these two components of motion are independent of each other
True
True or false: A projectile is an object upon which the only significant force is the force of gravity
True Ex: Doesn't have to have the horizontal component to be a projectile
True or false: A projectile could begin its projectile motion with a downward velocity
True Ex: Falling off a cliff
True or false: The time that a projectile is in the air is dependent upon the vertical component of the initial velocity
True Ex: If it takes three seconds to go up, it'll take three seconds to go down.
True or false: The final horizontal velocity of a projectile is always equal to the initial horizontal velocity
True Horizontal velocity is constant
True or false: The horizontal velocity of a projectile is unaffected by the vertical velocity; these two components of motion are independent of each other
True Only if Δy = 0 m
True or false: The horizontal displacement of a projectile is dependent upon the time of flight and the initial horizontal velocity
True Δx = Vx t
Is height a horizontal or vertical action?
Vertical
Δy
Vertical displacement Negative height of cliff
When Δy is 0 m...
Viy = Vfy
What are the acceleration vectors during projectile motion?
Vy decreases as the object moves upward and increases as the object moves downward. Vx stays constant.
What happens to my Δx value when I increase my angle to above or below 45°?
When the angle is either increased or decreased, the horizontal distance will decrease because changing the angle from 45° means that the projectile is getting closer to falling straight down in a vertical line. If θ>45° then Δx decreases because Vx is smaller If θ<45° then Δx decreases because time is smaller
Is speed a scalar?
Yes 75 km/hr
Is acceleration a vector?
Yes Ex: -9.80 m/s^2
Is distance a scalar?
Yes Ex: 150 miles
Is mass a scalar?
Yes Ex: 18 kg
An object is undergoing free fall motion. As it falls, the object's...
speed increases.
If an object returns to the same height as the launch position...
the vertical displacement is 0 m