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Solved problems for the chapter:

Acceleration due to Gravity

View the theory »

Vertical Motion under Gravity for KS4

1. Free fall acceleration

2. Description of free fall motion

2.1. Instantaneous/Final falling velocity

2.2. Height of fall

2.3. Time of fall

3. Forum

View the theory »

Vertical Motion under Gravity for A-Levels

1. Free fall

2. Vertical downward throw

3. Vertical upward throw

4. Forum

↓ Show theory [2] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:acceleration_due_to_gravity/4817/

Example 1.

A man stands in a lift that is accelerating vertically downwards, as shown

Which statement describes the force exerted by the man on the floor?

It is equal to the weight of the man.
It is greater than the force exerted by the floor on the man.
It is less than the force exerted by the floor on the man.
It is less than the weight of the man.

Example 2.

The symbol represents the acceleration of free fall. Which of these statements is correct?

is gravity.
is reduced by air resistance.
is the ratio weight/mass.
is the weight of an object.

An object falls from a stationary helicopter and reaches terminal velocity. What happens to the acceleration of the object between leaving the helicopter and reaching terminal velocity?

It decreases to .
It decreases to zero.
It increases to .
It remains constant at

An object is thrown with velocity vertically upwards on the Moon. The acceleration due to gravity on the Moon is . What is the time taken for the object to return to its starting point?

A stone is thrown vertically upwards from a point that is above the sea. It then falls into the sea below after . Air resistance is negligible. At which speed was the stone released when it was thrown?

A stone of mass m is dropped from a tall building. There is significant air resistance. The acceleration of free fall is . When the stone is falling at a constant (terminal) velocity, which information is correct?

	magnitude of the acceleration of the stone	magnitude of the force of gravity on the stone	magnitude of the force of air resistance on the stone
A		zero
B	zero
C	zero	zero
D	zero		zero

The diagram shows a laboratory experiment in which a feather falls from rest in a long evacuated vertical tube of length .

The feather takes time to fall from the top to the bottom of the tube. How far will the feather have fallen from the top of the tube in time ?

A girl throws a ball vertically upwards. It takes a time of to return to her hand. Assume air resistance is negligible. What is the initial speed with which the ball is thrown?

A body is released from rest and falls vertically in air of constant density. Which statement about the motion of the falling body is correct?

As it accelerates, its weight decreases so that its acceleration decreases until it travels with constant velocity.
It accelerates initially at but the drag force increases so its acceleration decreases.
Its velocity increases at a constant rate until its velocity becomes constant.
The drag force of the air increases continually and eventually the velocity decreases

10.

An experiment is performed to measure the acceleration of free fall . A body falls between two fixed points. The four measurements shown below are taken. Which measurement is not required for the calculation of ?

the distance fallen by the body
the initial velocity of the body
the mass of the body
the time taken for the body to fall

11.

A stone is released from rest and falls a long distance in air. Which graph could show the variation with time of the acceleration of the stone?

12.

An object is dropped from a great height and falls through air of uniform density. The acceleration of free fall is . Which graph could show the variation with time of the acceleration a of the object?

13.

A student takes a photograph of a steel ball of radius as it falls from rest. The image of the ball is blurred, as illustrated in the figure below. The image is blurred because the ball is moving while the photograph is being taken.

The scale shows the distance fallen from rest by the ball. At time , the top of the ball is level with the zero mark on the scale. Air resistance is negligible.

Calculate, to an appropriate number of significant figures,

the time the ball falls before the photograph is taken,
the time interval during which the photograph is taken.

14.

A boy throws a ball vertically upwards. It rises to a maximum height, where it is momentarily at rest, and falls back to his hands. Which of the following gives the acceleration of the ball at various stages in its motion? Take vertically upwards as positive. Neglect air resistance.

	rising	at maximum height	falling
A		0
B
C
D		0

15.

A small steel ball falls freely under gravity after being released from rest. Which graph best represents the variation of the height of the ball with time ?

16.

A stone is dropped from the top of a tower of height . The stone falls from rest and air resistance is negligible. What time is taken for the stone to fall the last to the ground?

17.

An object falls from a tall building. The graph shows how the velocity of the object changes with time .

The acceleration of free fall is . What describes the acceleration of the object at times and ?

	acceleration at	acceleration at
A	decreasing
B	decreasing	0
C	constant
D	constant	0

18.

A football is dropped from the top of a tall building. Which acceleration-time graph best represents the motion of the football through the air?

19.

A brick is dislodged from a building and falls vertically under gravity. Which graph best represents the variation of its height above the ground with time if air resistance is negligible?

20.

A student measures the time for a ball to fall from rest through a vertical distance . Knowing that the equation applies, the student plots the graph shown.

Which of the following is an explanation for the intercept on the axis?

Air resistance has not been taken into account for larger values of .
There is a constant delay between starting the timer and releasing the ball.
There is an error in the timer that consistently makes it run fast.
The student should have plotted against

21.

A body falls to the ground from a height of in . Is this movement a free fall?

22.

A ball is lowered from a great height. How deep did it fall between the 2nd and 4th seconds of the fall?

23.

From a certain height h, a body falls for 2 seconds. In how many seconds does it fall half the height?

24.

A stone is lowered into an abyss which is deep. How long does it take to hear the sound of the stone hitting the bottom of the abyss?

The speed of sound in air is .

25.

A stone drops to the ground from a height of . How far does it fall in the last second of the fall?

26.

An object falls through a high window in . From what height to the top edge of the window, does it fall?

27.

A body falls from rest.

By how much does the speed of the body increase every second?
What is the velocity of the body after ten seconds of falling?

28.

A body falls from rest. How long does it take the body to attain a final speed of 40 m/s and how deep has it fallen?

29.

A body has an initial velocity of 0 m/s. During free fall, its average velocity is 24 m/s. How deep does it fall?

30.

A stone falls freely from rest at a height of 140 m.

How far does the stone travel in the first second?
How far does it travel in the fifth second?
At what speed does it fall to the ground?

31.

A parachutist jumps out of the plane and falls freely for two seconds. He then opens the parachute and his speed is reduced to 2 m/s in 4 s.

Calculate his speed before he opens the parachute.
What is his deceleration after opening the parachute?
From what minimum height must the parachutist jump in order for him to land at a speed of 2 m/s?

32.

A stone is thrown vertically upwards at a speed of 10 m/s from a 60 m high bridge above a river. When it reaches its maximum height, it falls towards the river.

Where is the stone after 4 s of been thrown?
What is its speed at that time?

33.

A stone is thrown vertically downward to the ground from a height of 60 m.

What must be its initial velocity in order for it to hit the ground in 3 s?
What is its final velocity?

34.

A stone is dropped from a 20 m high balcony and at the same time, another stone is thrown vertically upwards from the ground with an initial velocity of 28 m/s. When are the stones at the same height to the ground and what is this height relative to the ground?

35.

A stone is thrown into a 40 m deep well with an initial speed of 4 m/s. How long does it take to hear a splash of water if the speed of sound is 340 m/s?

36.

A bullet is fired vertically upwards. It falls to the ground after 6 s.

What are the initial and final velocities of the bullet?
What is the maximum height of the bullet?

37.

A flower falls from a window sill at the top floor of a high-rise building. Jack watches the flower as it falls past his window. Jack's window is 1.6 m high and the flower falls past it in 0.1 s.

What is the speed of the flower at the top and bottom edge of Jack's window?
From what height, relative to the top edge of Jack's window, does the flower fall?

38.

A stone is thrown vertically downwards from a height of 40 m with an initial speed of 2 m/s. At the same time, another stone is thrown vertically upwards with a speed of 34 m/s. What is the speed of each of the two stones when they are at the same height to the ground?