Conceptual Physics: Freefall and Simple Motion

What equation can calculate future velocity without knowing time?

(Future Velocity)^2 = (Initial Velocity)^2 + 2(Acceleration)(Displacement)

Two balls are thrown from the top of a building, as in the drawing. Ball 1 is thrown straight down, and Ball 2 is thrown with the same speed, but upward at an angle θ with respect to the horizontal. Consider the motion of the balls after they are released. Which one of the following statements is true knowing if both balls are in freefall? A) Both balls have the same acceleration at all times. B) The acceleration of ball 1 becomes larger and larger as it falls because the ball is going faster and faster. C) The acceleration of ball 2 decreases as it rises, becomes zero at the top of the trajectory, and then increases as the ball begins to fall toward the ground. D) Ball 2 has an acceleration in both the horizontal and vertical directions, but ball 1 has an acceleration only in the vertical direction.

A) Both balls have the same acceleration at all times. If we look at the projectile motion of Ball 2 by its horizontal and vertical components, we can observe that the acceleration of the y-component is a = -9.8 m/s^2 (vertical motion of projectile motion has constant acceleration) while the acceleration of the x-component is a= 0. Meanwhile, Ball 1 is moving only vertically downwards and has an acceleration of a = -9.8 m/s^2.

A bicyclist is moving at a constant speed along a straight-line path. The rider throws a ball straight up to a height a few meters above her head. Ignoring air resistance, where will the ball land? A) In the same hand that threw the ball. B) In the opposite hand of the hand that threw the ball. C) Behind the rider. D) In front of the rider. E) There's not enough information without knowing the speed of the rider and the maximum height of the ball.

A) In the same hand that threw the ball. The motion of the ball and the rider can be modeled as two straight lines. When the rider threw the ball, the ball inherited the velocity of the rider from that time it was thrown. Since the rider is riding at a constant speed, the ball is going to follow the rider and land into the exact same hand.

What did Aristotle and Galileo think of free falling bodies? Who was correct?

Aristotle thought heavier bodies fall faster than lighter bodies in proportion to their weight. This was proven wrong by Galileo showing that all bodies in freefall fall at the same rate (acceleration).

An object at rest near the surface of a distant planet starts to fall freely. If the acceleration there is twice that of the Earth, its speed two seconds later would be: A) 19.6 m/s B) 29.4 m/s C) 58.8 m/s D) 39.2 m/s

D) 39.2 m/s Step 1: We know that the a = (2)(-9.8 m/s^2) = -19.6 m/s^2, Initial Velocity = 0 m/s, and t = 2 seconds. Use: Future Velocity = Initial Velocity + (Time)(Acceleration) Step 2: Future Velocity = 0 m/s + (-19.6 m/s^2)(2 sec) Step 3: Future Velocity = -39.2 m/s Since we are looking for speed, our final answer can not be negative, so the speed is 39.2.

If an object falling freely were somehow equipped with an odometer to measure the distance it travels, then the amount of distance it travels each succeeding second would be: A) Constant B) Doubled C) Less and less each second D) Greater than the second before

D) Greater than the second before

Which statement is true concerning to a ball when it is at the highest point in its trajectory? A) The ball's velocity and acceleration are both zero. B) The horizontal and vertical components of the ball's velocity are equal. C) The ball's velocity is zero, but its acceleration is not zero. D) The ball's velocity is perpendicular to its acceleration. E) The ball's velocity is not zero, but its acceleration is zero.

D) The ball's velocity is perpendicular to its acceleration.

Heavier objects fall faster than lighter objects. True or False?

False.

You can launch a projectile with a fixed initial speed but at any angle above the horizontal, and it feels no air resistance. The time for it to return to the ground does not depend on the angle at which you launch it. True or False?

False.

The velocity of a freely falling bowling ball decreases each second by 9.8 m/s. True or False?

False. Since the acceleration of any freely falling object is a = 9.8 m/s^2 and acceleration is the change in velocity in relation to time, velocity must be increasing at a rate of 9.8 m/s.

What is the difference between terminal speed and velocity?

Terminal velocity is the same as terminal speed, but the direction is implied or specified.

An object is thrown off of a cliff. If an object is moving downwards in freefall, is the acceleration constant (a = 9.8 m/s^2) positive or negative? If the velocity of the object is 30 m/s, is that positive or negative?

The acceleration constant and the velocity are both negative. We look at this by dividing the motion of the object into a coordinate system. If the top of the cliff represents the x-axis and the height is represented as the y-axis, then acceleration is negative due to the force of gravity pulling downward. Likewise, the velocity is also negative because of the direction pointing downward.

An object is thrown off of a cliff. If an object is moving upwards in freefall, is the acceleration constant (a = 9.8 m/s^2) positive or negative? If the velocity of the object is 30 m/s, is that positive or negative?

The acceleration constant is negative and the velocity is positive. We look at this by dividing the motion of the object into a coordinate system. If the top of the cliff represents the x-axis and the height is represented as the y-axis, then acceleration is negative due to the force of gravity pulling downward. On the other hand, velocity is positive because of the direction pointing upward.

A hunter on level ground fires a bullet at an angle of 10 degrees above the horizontal while simultaneously dropping another bullet from the level of the rifle. Which bullet will hit the ground first?

The one that dropped.

A spring-loaded gun is aimed horizontally and is used to launch identical balls with different initial speeds. The gun is at a fixed position above the floor. The balls are fired one at a time. If the speed of the second ball fired is twice the speed of the first ball fired, how is the horizontal range affected?

The range of the second ball will be twice as large as the first ball.

What happens when you launch projectiles at varying angles (providing the initial velocity is the same)?

You get different horizontal distances.

What is the constant of acceleration for any object in freefall?

a = 9.8 m/s^2

What is the condition of non-freefall?

- Air resistance is non-negligible.

What are the criteria for an object to be in freefall?

- Can only be falling under the influence of gravity. - Negligible air drag/resistence

What factors impact the amount of air resistance on an object during non-freefall?

- Speed - Frontal Surface Area of the Object

During non-freefall, when the object is moving fast enough so that air resistance builds up to equal the force of gravity, what happens?

- There's no net force. - No acceleration. - Velocity does not change.

A projectile is fired into the air at an angle of 65° above ground level and hits a target downrange. It will also hit the target if fired at an angle of:

25 degrees. (90 - 65 degrees = 25 degrees)

A projectile fired at 5 m/s from a gun. If the horizontal component of the initial velocity is equal to 4 m/s. What is the value of the vertical component?

3 m/s (using r^2 = h^2 + v^2)

How do find another equivalent launch angle for projectile motion providing that both are launched at the same initial speed?

90 - θ = equivalent launch angle

An apple falls 5 m from a tree. What is the speed when it hits the ground? A) 9.89 m/s B) 4.89 m/s C) 19.6 m/s D) 49.0 m/s

B) 4.89 m/s We know that a = -9.8 m/s^2 (negative due to gravity), Intital velocity = 0 m/s, and x (displacement) = 5 m. Use: (Future Velocity)^2 = (Intital Velocity)^2 + 2(Acceleration)(Displacement) (Future Velocity)^2 = (0 m/s)^2 + 2(-9.8 m/s^2)(5 m) (Future Velocity)^2 = 2(-9.8 m/s^2)(5 m) (Future Velocity)^2 = (-19.6 m/s^2)(5 m) (Future Velocity)^2 = - 98 m/s Future Velocity ≈ -9.89 m/s Since we are looking for speed, our final answer can not be negative, so the speed is 9.89 m/s.

The distance a freely falling bowling ball falls each second: A) Is about 5 m B) Increases C) Is about 10 m D) None of the above

B) Increases

A ball is thrown upwards and returns to the same location. Compared with its initial speed its speed when it returns is about: A) Twice as much B) The same C) Half as much D) Four times as much

B) The same

If a freely falling object were equipped with a speedometer on a planet where the acceleration due to gravity is 20 m/s^2, then its speed reading would increase each second by: A) 30 m/s B) 40 m/s C) 20 m/s D) 10 m/s

C) 20 m/s

A bicyclist is speeding up along a straight-line path. The rider throws a ball straight up to a height a few meters above her head. Ignoring air resistance, where will the ball land? A) In the same hand that threw the ball. B) In the opposite hand of the hand that threw the ball. C) Behind the rider. D) In front of the rider. E) There's not enough information without knowing the speed of the rider and the maximum height of the ball.

C) Behind the rider. The motion of the ball and the rider can be modeled as two straight lines. When the rider threw the ball, the ball inherited the velocity of the rider from that time it was thrown. Since the rider is constantly speeding up, the speed of the rider is going to outpace the ball.

What is the equation to calculate the change in position of an object?

Change in position = Initial Position + (Time)(Velocity) + 0.5(Acceleration)(Time)^2

While a rock thrown upward at 50 degrees to the horizontal rises, neglecting air drag, its vertical component of velocity:

Decreases.

What is the equation to find the distance covered by an accelerating object starting at rest?

Distance = 0.5(Acceleration)(Time)^2

When does terminal speed occur? What happens afterward?

During non-freefall, this occurs when acceleration terminates, air resistance is equal to the object's weight, and the net force is zero. After this happens, the object falls at a constant speed.

A football is kicked toward the goalposts and feels no air resistance. While it is in the air, the only force acting on it is 9.8 m/s^2. True or False?

False. Even if we ignore the impulsive force of thrust, there's an applied force

A grasshopper leaps into the air at a 62-degree angle above the horizontal. At its highest point, the grasshopper's velocity and acceleration are equal to zero. True or False?

False. Only the vertical velocity is zero while the vertical acceleration is -g in projectile motion.

What is the equation to calculate a future velocity at a later time?

Future Velocity = Initial Velocity + (Time)(Acceleration)

What is the relationship between gravity and mass?

Mass and gravity are directly proportional. If gravity increased, then the mass also increases, and vice versa.

While a rock thrown upward at 50 degrees to the horizontal rises, neglecting air drag, its horizontal component of velocity:

Remains unchanged.

A tennis ball is thrown upwards from an edge of a cliff with a speed of 10 m/s. It lands on the ground below the cliff 30 seconds later. We can ignore air resistance. What is the displacement of the tennis ball?

Step 1: We know that Initial Velocity = 10 m/s (positive since the ball is thrown upward), a = -9.8 m/s^2 (negative due to gravity), and t = 3 seconds Use: Displacement = (Initial Velocity)(Time) + 0.5(acceleration)(time)^2 Step 2: Displacement = (10 m/s)(3 sec) + 0.5(-9.8 m/s^2)(3 sec)^2 Step 3: Displacement = 30 m + 0.5(-88.2 m) Step 4: Displacement = 30 m + -44.1 m Step 5: Displacement = -14.1 m

An object is moving in freefall is moving upward at 50 m/s. What is its speed one second later?

Step 1: We know that a = -9.8 m/s^2 (negative due to gravity), Initial velocity = 50 m/s (positive because the object is moving upward), and t = 1 second. Use: Future Velocity = Initial Velocity + (Time)(Acceleration) Step 2: Future Velocity = 50 m/s + (1 sec)(-9.8 m/s^2) Step 3: Future Velocity = 40.2 m/s The speed is 40.2 m/s

What is the simplest kind of motion?

The simplest kind of motion is a straight-line motion with constant acceleration and a velocity that changes at the same rate throughout the motion.

Objects can be in freefall going upward. True or False?

True.

Without air resistance, the time for a projectile to reach its maximum height is the same as the time for it to return to the ground. True or False?

True.

A ball is thrown at an angle above the horizontal from the top of a cliff and feels no air resistance. A runner at the base of the cliff moves horizontally so that she is always under the ball. In this runner's reference frame, the path of the ball is a straight line rather than a parabola. True or False?

True. If we look at the projectile motion of the ball by its horizontal and vertical components, we can observe that the runner and the ball's horizontal motion are the same. This is due to the runner running underneath the ball, which means that the ball and the runner have the same velocity. Their horizontal motion can be represented as a straight line from the runner's reference frame.