 ### Falling Bodies Questions

Click the question to get the solutions, including videos.
March 2013

3 A ball of mass 0,2kg is dropped from a height of 0,8m onto a hard floor. It bounces to a maximum height of 0,6m. The floor exerts a force of 50 N on the ball. Ignore the effects of friction.

3.1 Write down the magnitude and direction of the force that the ball exerts on the floor. (2)
3.1   50N

3.2 Calculate the:

3.2.1 Velocity at which the ball strikes the floor (4)
3.2.1 3.2.2 Time that the ball is in contact with the floor if it bounces off the floor at a speed
of 3,43 m.s-1 (4)
3.2.2 3.3 The ball takes 0,404s from the moment it is dropped until it strikes the floor. Sketch a graph (not to scale) of position versus time representing the entire motion of the ball.
USE THE GROUND AS ZERO REFERENCE.

Indicate the following on the graph:
• Height from which the ball is dropped
• Height reached by the ball after the bounce
• Time at which the ball bounces off the floor (5)
3.3
OPTION 1
Ground as zero reference and downward negative: OPTION 2
Ground as zero reference and downward positive: March 2012

3 A stone is thrown vertically upward at a velocity of 10ms-1 from the top of a tower of height 50m. After some time the stone passes the edge of the tower and strikes the ground below the tower. Ignore the effects of friction. 3.1 Draw a labelled free-body diagram showing the force(s) acting on the stone during its motion. (1)
3.1 3.2 Calculate the:

3.2.1 Time taken by the stone to reach its maximum height above the ground (4)
3.2.1 3.2.2 Maximum height that the stone reaches above the ground (4)
3.2.2 3.3 USING THE GROUND AS REFERENCE (zero position), sketch a positiontime graph for the entire motion of the stone. (3)
3.3 OR 3.4 On its way down, the stone takes 0,1s to pass a window of length 1,5m, as shown in the diagram above. Calculate the distance (y1) from the top of the window to the ground. (7)
3.4
Calculate the initial velocity at which it reached the top of the window. Use this velocity as the final velocity from the highest point to this point.  Nov 2012

3 An object is projected vertically upwards at 8 m.s-1 from the roof of a building which is 60m high. It strikes the balcony below after 4s. The object then bounces off the balcony and strikes the ground as illustrated below. Ignore the effects of friction. 3.1 Is the object's acceleration at its maximum height UPWARD, DOWNWARD or ZERO? (1)
3.1 Downward

3.2 Calculate the:

3.2.1 Magnitude of the velocity at which the object strikes the balcony (4)
3.2.1 3.2.2 Height, h, of the balcony above the ground (5)
3.2.2 The object bounces off the balcony at a velocity of 27,13 m.s-1 and strikes the ground 6s after leaving the balcony.

3.3 Sketch a velocity-time graph to represent the motion of the object from the moment it is projected from the ROOF of the building until it strikes the GROUND.
Indicate the following velocity and time values on the graph:

• The initial velocity at which the object was projected from the roof of the building
• The velocity at which the object strikes the balcony
• The time when the object strikes the balcony
• The velocity at which the object bounces off the balcony
• The time when the object strikes the ground (6)
3.3 March 2011

3 The velocity-time graph shown below represents the motion of two objects, A and B, released from the same height. Object A is released from REST and at the same instant object B is PROJECTED vertically upwards. (Ignore the effects of friction.) 3.1 Object A undergoes a constant acceleration. Give a reason for this statement by referring to the graph. (No calculations are required.) (2)
3.1 Gradient of the graph is constant.

3.2 At what time / times is the SPEED of object B equal to 10 m.s-1? (2)
3.2   At t = 1s and t = 3s

3.3 What is the velocity of object A relative to object B at t = 1s? (3)
3.3 3.4 Object A strikes the ground after 4s. USE EQUATIONS OF MOTION to calculate the height from which the objects were released. (3)
3.4 The reason why 10m.s-2 OR 9,8m.s-2 was allowed, is that the acceleration is 10m.s-2 from the graph.

3.5 What physical quantity is represented by the area between the graph and the time axis for each of the graphs A and B? (2)
3.5
Displacement

OR

Change in position

3.6 Calculate, WITHOUT USING EQUATIONS OF MOTION, the distance between objects A and B at t = 1s. (5)
3.6 Nov 2011

3 A hot-air balloon is moving vertically upwards at a constant speed. A camera is accidentally dropped from the balloon at a height of 92,4m as shown in the diagram below. The camera strikes the ground after 6s. Ignore the effects of friction. 3.1 At the instant the camera is dropped, it moves upwards. Give a reason for this observation. (1)
3.1 The initial velocity (speed) of the camera is the same as that of the balloon. (upwards)

3.2 Calculate the speed vi at which the balloon is rising when the camera is dropped. (4)
3.2 The balloon speed would be the initial velocity of the camera.
For the camera, use the the dispacment of 92,4m but the full time of 6 seconds. The initial velocity thus calculated would be the answer since this accomodates the full 6 seconds of up and down, and NOT the time to actually fall the 92,4m.

3.3 Draw a sketch graph of velocity versus time for the entire motion of the camera.

Indicate the following on the graph:
• Initial velocity
• Time at which it reaches the ground (4)
3.3 3.4 If a jogger, 10m away from point P as shown in the above diagram and running at a constant speed of 2m.s-1, sees the camera at the same instant it starts falling from the balloon, will he be able to catch the camera before it strikes the ground?
Use a calculation to show how you arrived at the answer. (5)
3.4 It is understodd that the jogger will get there first, and wait to catch the camera.

March 2010

5 A supervisor, 1,8 m tall, visits a construction site. A brick resting at the edge of a roof 50 m above the ground suddenly falls. At the instant when the brick has fallen 30m the supervisor sees the brick coming down directly towards him from above.

Ignore the effects of friction and take the downwards motion as positive.

5.1 Calculate the speed of the brick after it has fallen 30 m. (3)
5.1 5.2 The average reaction time of a human being is 0,4s. With the aid of a suitable calculation, determine whether the supervisor will be able to avoid being hit by the brick. (6)
Velocity after a further 18,2m: He will not be struck
His reaction time is shorter than the time for the brick to reach his head.

Reaction Time is the delay you experience from when you saw something, till you actually react.

Nov 2010

3 A man fires a projectile X vertically upwards at a velocity of 29,4 m.s-1 from the EDGE of a cliff of height 100m. After some time the projectile lands on the ground below the cliff. The velocity-time graph below (NOT DRAWN TO SCALE) represents the motion of projectile X. (Ignore the effects of friction.) 3.1 Use the graph to determine the time that the projectile takes to reach its maximum height. (A calculation is not required.) (1)
3.1 3 seconds

3.2 Calculate the maximum height that projectile X reaches above the ground. (4)
3.2 Area between graph and time axis 3.3 Sketch the position-time graph for projectile X for the period t = 0s to t = 6s.
USE THE EDGE OF THE CLIFF AS ZERO OF POSITION.

Indicate the following on the graph:
• The time when projectile X reaches its maximum height
• The time when projectile X reaches the edge of the cliff (4)
3.3 3.4 One second (1s) after projectile X is fired, the man's friend fires a second projectile Y upwards at a velocity of 49m.s-1 FROM THE GROUND BELOW THE CLIFF.
The first projectile, X, passes projectile Y 5,23 s after projectile X is fired.
(Ignore the effects of friction.)
Calculate the following:

3.4.1 The velocity of projectile X at the instant it passes projectile Y (5)
3.4.1 3.4.2 The velocity of projectile X RELATIVE to projectile Y at the instant it passes projectile Y (5)
3.4.2 March 2009

5 The roof of a tall building is 25m above the ground. A rigid ball of mass 0,3kg falls freely when dropped from the roof. It strikes the concrete floor on the ground with velocity v1. It bounces to a maximum vertical height of 6m. The ball was in contact with the floor for 0,9s. Ignore the effects of friction. 5.1 Calculate the velocity v1 when the ball first hits the floor. (3)
5.1 5.2 Calculate the impulse of the ball as a result of the collision. (7)
5.2 Consider upward motion as positive: Then 5.3 Calculate the magnitude of the net force exerted on the ball. (3)
5.3 Take upward as positive: 5.4 Using the ground as zero reference, draw a sketch graph of position (displacement) versus time for the motion of the ball from its original height until it reaches its second maximum height. Indicate the relevant position values on the y-axis. (4)
5.4 5.5 The rigid ball is now replaced with a softer ball of the same mass and volume as the rigid ball. It is then dropped from the same height onto the concrete floor.
Will the ball reach the SAME, GREATER or LESSER height compared to the previous ball? Use principles of physics to explain your answer. (3)
5.5 Smaller
Contact time for softer ball is longer than for rigid ball.
According to FnetΔt = Δp, the force exerted by floor on softer ball is smaller than on the rigid ball.

Nov 2009 Unused

4 A ball is released from a certain height. The velocity-time graph below represents the motion of the ball as it bounces vertically on a concrete floor. The interaction time of the ball with the floor is negligibly small and is thus ignored. 4.1 Describe the changes, if any, in velocity and acceleration of the ball
from t = 0s to t = 0,4s. (4)
4.1
at t = 0s:
ball starts from rest (0 m.s-1)

from t = 0s - 0,4s:
• falls at constant acceleration
• constant increase in velocity

at t = 0,4s:
• reaches the floor at 4m.s-1 (or 4m.s-1 downwards)

at t = 0,4s:
• bounces back at -3m.s-1 (or 3m.s-1 upwards)

4.2 Without using the equations of motion, calculate the height from which the ball has been dropped initially. (4)
4.2 To find the distance from a v-t graph, calculate the area under the graph. Use the given velocity versus time graph for the motion of the ball to sketch the corresponding position-time graph for the time interval 0s to 0,7s. (3)
4.3 4.4 Is the first collision of the ball with the floor elastic or inelastic? Give a reason for your answer. (2)
4.4 Inelastic
Decrease / change in speed (from 4m.s-1 to 3m.s-1)

OR

Decrease/change in kinetic energy during collision

Nov 2009

4 The following extract comes from an article in a school newspaper.

THE LAWS OF PHYSICS ARE ACCURATE!
Two construction workers, Alex and Pete, were arguing about whether a smaller brick would hit the ground quicker than a larger brick when both are released from the same height.

Alex said that the larger brick should hit the ground first. Pete argued that the smaller brick would hit the ground first.

4.1 Are their statements correct? Give a reason for your answer. (3)
4.1
Option 1
Statements not correct
The bricks will experience the same gravitational acceleration of free fall and thus reach the ground at the same time.

Option 2
Pete is correct or Alex is wrong.
The smaller brick experiences less air resistance, thus larger acceleration and reaches the ground first.

Option 3
Alex is correct or Pete is wrong.
In the presence of air resistance, the larger brick, with larger mass, experiences a larger net force downwards, thus largest acceleration and reaches the ground first.

Option 4
Both are correct.
Pete correct: The smaller brick experiences less air resistance, thus larger acceleration and reaches the ground first.
Alex correct: In the presence of air resistance, the larger brick, with larger mass, experiences a larger net force downwards, thus largest acceleration and reaches the ground first.

Option 1 deals with a free fall situation. Options 2, 3, and 4 deals with air resistance present. Option 1 is the best answer with what this question intended.

4.2 A group of Physical Sciences learners decide to test Alex's and Pete's hypotheses. They drop two bricks, one small and the other much larger, from one of the floors of the school building.

4.2.1 Write down TWO precautions they should take to ensure that the result is reliable. (2)
4.2.1 Any two
• Ensure that both bricks are dropped from same height
• Ensure that both bricks are dropped at the same time
• Ensure that the stopwatch starts at instant that each brick is released and stopped at the instant that each brick reaches the ground
• Repeat the experiment several times and use the average of the results
• Make sure that vi = 0 for both bricks
• Make sure that there is no strong wind
• Use bricks made of the same material / of same density

4.2.2 Give a reason why, despite all the necessary precautions, they might not get the correct result. (1)
4.2.2 External force(s) may be present e.g. friction / air resistance / strong wind blowing

4.3 In another experiment, the learners drop a brick A from a height of 8 m. After 0,6s, they throw a second brick B downwards from the same height. Both bricks, A and B, hit the ground at the same time.

Ignore the effects of friction and calculate the speed at which brick B was thrown. (7)
4.3 Nov 2008

6 A boy stands at the edge of a high cliff. He throws a stone vertically upwards with an initial velocity of 10m.s-1. The stone strikes the ground at a point below the cliff after 3,5s. The velocity-time graph below was obtained from measurements made during the motion of the stone. Use the information on the graph to answer the following questions:

6.1 Calculate the acceleration of the stone between times t = 2 s and t = 3 s. (3)
6.1 6.2 At which time(s) is the stone moving at a speed of 5m.s-1? (2)
6.2   0,5s and 1,5s

6.3 After how many seconds does the stone reach its highest point? (1)
6.3   1s

6.4 Determine the height of the cliff from which the stone was thrown. (4)
6.4 Difference between areas of two triangles 6.5 Using the top of the cliff as the initial position of the stone, sketch the position-time graph (displacement-time graph) for the motion of the stone from its highest point until it reaches the ground. Only indicate relevant time values on the x-axis. (3)
6.5 Prep Paper 2008

5.1 Marshall stands on a platform and kicks a soccer ball from 6m above the ground (position A) vertically upwards into the air with an initial velocity of 4 m.s-1. The ball hits the ground (position D) after 1,6 seconds. The motion of the ball is represented in the diagram below. Ignore the effects of air resistance. 5.1 Calculate the maximum height (position B) the ball reaches above the ground. (5)
5.1 Consider upward motion as positive 5.2 Calculate the time taken for the ball to reach maximum height (position B). (3)
5.2 Consider upward motion as positive: 5.3 Draw a sketch graph of position versus time for the motion of the ball from the moment it was kicked until it hits the ground. Use point A as the reference point (zero-position). Indicate ALL relevant position and time values at positions A, B, C and D. (5)
5.3
up as positive Exemplar Paper 2008

5 A hot-air balloon is rising vertically at constant velocity. When the balloon is at a height of 88m above the ground, a stone is released from it. The displacement-time graph below represents the motion of the stone from the moment it is released from the balloon until it strikes the ground. Ignore the effect of air resistance. Use information from the graph to answer the following questions:

5.1 Calculate the velocity of the hot-air balloon at the instant the stone is released. (6)
5.1
Considering upward motion only
Upward motion positive OR

For complete motion of stone
Upward motion positive 5.2 Draw a sketch graph of velocity versus time for the motion of the stone from the moment it is released from the balloon until it strikes the ground. Indicate the respective values of the intercepts on your velocity-time graph. (3)
5.2 Upward motion as positive: 5 Any falling object which is being acted upon only by the force of gravity is said to be in a state of free fall.

5.1 Briefly describe how you can make use of a small free-falling stone to determine how deep the water level is in a well (represented by y in the diagram below). 5.1
• Release a stone from the top of the well and let it fall straight down into the well.
• Take the time from it was released until it splashes in the water.
• Use the equation: with vi = 0 to calculate the depth of the water level.

5.2 Give ONE reason why the concept of free fall might not give a correct answer. (1)
5.2 Due to air friction, gravity is not the only force acting on the object.

5.3 A student is at the top of a building of height h. He throws a stone, X, upward with a speed v. He then throws a second identical stone, Y, downward at the same speed v.

5.3.1 Redraw the following set of axes in the ANSWER BOOK and sketch the graphs of position versus time for each of the stones X and Y. Use the ground as the point of zero position. 5.3.1 5.3.2 How will the velocities of the two stones, X and Y, compare when they reach the ground? Explain your answer.
5.3.2 Velocities will be the same.
 Both X and Y experience the same displacement and same acceleration. On its downward flight X has same velocity as Y at a height of h.

Using: will thus give the same final velocity for both. 

5.4 A mountain climber stands at the top of a 50m cliff that overhangs a calm pool. She throws two stones vertically downward 1s apart and observes that the two stones reach the water simultaneously after a while. The first stone was thrown at an initial speed of 2 m.s-1.

Calculate the initial speed at which she threw the second stone. Ignore the effects of friction.
5.4
For X - downwards as positive For Y - downwards as positive ----------------------------------