Motion Under Gravity — Advanced Practice

Section A: Foundations

Question 1mcq

Taking upward as positive, what is the acceleration of a freely moving body near Earth after it has been projected upward?

A.

-g

B.

+g

C.

0

D.

+2g

Question 2mcq

A stone is dropped from rest. Which equation gives its speed after time

t

if downward is taken as positive?

A.

v=-gt

B.

v=gt

C.

v=g/t

D.

v=t/g

Question 3mcq

A ball is thrown vertically upward with speed

20\,m/s

. Using

g=10\,m/s^2

, the time taken to reach the highest point is?

A.

1\,s

B.

4\,s

C.

2\,s

D.

20\,s

Question 4mcq

For a body thrown vertically upward and returning to the same level without air resistance, which statement is correct?

A.Time of ascent is twice time of descent.

B.Time of descent is always zero.

C.The two times are unrelated.

D.Time of ascent equals time of descent.

Question 5mcq

A body is dropped from rest for

3\,s

. Using

g=10\,m/s^2

, its speed is?

A.

30\,m/s

B.

15\,m/s

C.

45\,m/s

D.

90\,m/s

Question 6mcq

A ball is thrown upward with speed

30\,m/s

. What is its velocity after

1\,s

if upward is positive and

g=10\,m/s^2

?

A.

40\,m/s

B.

20\,m/s

C.

-20\,m/s

D.

10\,m/s

Question 7mcq

A ball reaches the highest point of its path. Which quantity is zero at that instant?

A.Acceleration due to gravity

B.Mass

C.Instantaneous velocity

D.Gravitational force

Question 8mcq

A stone is moving downward while upward is chosen positive. Which sign combination is correct?

A.Velocity positive, acceleration negative

B.Velocity negative, acceleration positive

C.Both zero

D.Velocity negative, acceleration negative

Question 9mcq

A body is dropped from a height. Which of the following remains constant during ideal free fall?

A.Acceleration

B.Velocity

C.Distance covered each second

D.Kinetic energy

Question 10mcq

A ball is thrown upward with speed

u

. Its maximum height above the point of projection is?

A.

\frac{u}{g}

B.

\frac{u^2}{2g}

C.

2ug

D.

\frac{g^2}{2u}

Section B: Core Applications

Question 11mcq

A ball is thrown upward at

25\,m/s

. Using

g=10\,m/s^2

, what is its velocity after

4\,s

if upward is positive?

A.

15\,m/s

B.

-40\,m/s

C.

-15\,m/s

D.

65\,m/s

Question 12mcq

A stone is dropped from a tower and reaches the ground in

4\,s

. Using

g=10\,m/s^2

, the tower height is?

A.

40\,m

B.

160\,m

C.

20\,m

D.

80\,m

Question 13mcq

A ball is thrown vertically upward at

40\,m/s

. Using

g=10\,m/s^2

, its maximum height is?

A.

80\,m

B.

40\,m

C.

160\,m

D.

20\,m

Question 14mcq

A stone is dropped from rest. What distance does it cover during the third second? Take

g=10\,m/s^2

.

A.

15\,m

B.

25\,m

C.

30\,m

D.

45\,m

Question 15mcq

Two stones are dropped from the same point

1\,s

apart. Three seconds after the first stone is released, their separation is? Take

g=10\,m/s^2

.

A.

15\,m

B.

35\,m

C.

25\,m

D.

45\,m

Question 16mcq

A ball is thrown upward from the ground at

30\,m/s

. At what two times is it at a height of

40\,m

? Take

g=10\,m/s^2

.

A.

1\,s

and

5\,s

B.

2\,s

and

3\,s

C.

3\,s

and

6\,s

D.

2\,s

and

4\,s

Question 17mcq

A body is thrown downward from a tower with speed

5\,m/s

and reaches the ground in

3\,s

. Take downward positive and

g=10\,m/s^2

. The height is?

A.

60\,m

B.

45\,m

C.

50\,m

D.

90\,m

Question 18mcq

A ball thrown upward returns to the launch point after

6\,s

. With

g=10\,m/s^2

, its launch speed is?

A.

60\,m/s

B.

30\,m/s

C.

15\,m/s

D.

20\,m/s

Question 19mcq

A stone is dropped from a balloon rising upward at

10\,m/s

. What is the stone’s initial velocity relative to the ground just after release?

A.

0

B.

10\,m/s

downward

C.

10\,m/s

upward

D.

20\,m/s

upward

Question 20mcq

A body covers

35\,m

in the fourth second of free fall. Using

s_n=\frac{g}{2}(2n-1)

, what value of

g

is implied?

A.

5\,m/s^2

B.

7\,m/s^2

C.

14\,m/s^2

D.

10\,m/s^2

Question 21mcq

A stone falls from rest and covers

45\,m

in the last second. Take

g=10\,m/s^2

. What is the total fall time?

A.

5\,s

B.

4\,s

C.

6\,s

D.

9\,s

Question 22mcq

Two balls are projected vertically upward with speeds in the ratio

2:3

. Their maximum heights are in the ratio?

A.

2:3

B.

4:9

C.

3:2

D.

8:27

Question 23mcq

A ball thrown upward passes the same height at

1\,s

and

5\,s

. With

g=10\,m/s^2

, what was its initial speed?

A.

20\,m/s

B.

40\,m/s

C.

30\,m/s

D.

60\,m/s

Question 24mcq

A stone is dropped from a tower while another is projected upward from the ground at

20\,m/s

. If the tower is

30\,m

high, when do they meet?

A.

1\,s

B.

2\,s

C.

3\,s

D.

1.5\,s

Question 25mcq

Assertion: At the highest point of vertical motion, velocity is zero. Reason: Acceleration is also zero there. Which option is correct?

A.Assertion is true, but reason is false.

B.Both are true and reason explains assertion.

C.Both are true but reason does not explain assertion.

D.Assertion is false, but reason is true.

Section C: Advanced Reasoning

Question 26mcq

A body dropped from rest covers

7/16

of its total height in the last second. What is the total time of fall?

A.

3\,s

B.

4\,s

C.

5\,s

D.

6\,s

Question 27mcq

A ball is projected upward from the top of a

45\,m

tower at

10\,m/s

. Take

g=10\,m/s^2

. Its speed on reaching the ground is?

A.

20\,m/s

B.

30\,m/s

C.

10\sqrt{10}\,m/s

D.

10\sqrt{5}\,m/s

Question 28mcq

A stone is dropped from height

H

. The time taken to cover the first half is

t_1

and the second half is

t_2

. Which relation is correct?

A.

t_2=t_1

B.

t_2=\sqrt2t_1

C.

t_1=(\sqrt2-1)t_2

D.

t_2=(\sqrt2-1)t_1

Question 29mcq

A balloon rises at

15\,m/s

. A stone is released when the balloon is

80\,m

above ground. Take

g=10\,m/s^2

. After how long does the stone hit the ground?

A.

5\,s

B.

4\,s

C.

6\,s

D.

8\,s

Question 30mcq

A body is thrown vertically upward with speed

u

. What distance does it travel during the last second of ascent?

A.

u-\frac{g}{2}

B.

\frac{g}{2}

C.

g

D.

u-g

Question 31mcq

A rocket has net upward acceleration

10\,m/s^2

for

60\,s

, then moves only under gravity with

g=10\,m/s^2

. Its maximum height from launch is?

A.

18\,km

B.

54\,km

C.

36\,km

D.

72\,km

Question 32mcq

A stone is projected upward from the ground with speed

40\,m/s

. At the same instant another stone is dropped from a height of

100\,m

. When do they meet? Take

g=10\,m/s^2

.

A.

2\,s

B.

4\,s

C.

5\,s

D.

2.5\,s

Section D: Challenge Set

Question 33mcq

A body is projected upward at

50\,m/s

. What is the ratio of distances travelled in the first second and the last second of ascent? Take

g=10\,m/s^2

.

A.

9:1

B.

5:1

C.

1:9

D.

4:1

Question 34mcq

A ball is thrown upward with speed

30\,m/s

from a roof

20\,m

above ground. How long until it reaches the ground? Take

g=10\,m/s^2

.

A.

3-\sqrt{13}\,s

B.

3+\sqrt{13}\,s

C.

\sqrt{13}\,s

D.

6\,s

Question 35mcq

A body is dropped from height

125\,m

. During which second does it cover the greatest distance? Take

g=10\,m/s^2

.

A.The first second

B.The third second

C.The fifth second

D.All seconds equally

Question 36mcq

Two bodies are projected vertically upward from the same point with speeds

20\,m/s

and

30\,m/s

. After how much time is their separation

15\,m

while both are moving?

A.

1\,s

B.

2\,s

C.

3\,s

D.

1.5\,s

Question 37mcq

A particle is projected upward and is at the same height at times

2\,s

and

6\,s

. With

g=10\,m/s^2

, what is that height above the launch point?

A.

60\,m

B.

40\,m

C.

80\,m

D.

120\,m

Question 38mcq

A body dropped from rest takes total time

T

. What fraction of total height is covered in the final half of the total time?

A.

\frac12

B.

\frac34

C.

\frac14

D.

\frac78

Question 39mcq

A ball is projected upward from ground at

30\,m/s

. Another ball is projected upward from the same point

2\,s

later at

50\,m/s

. When after the second launch do they meet? Take

g=10\,m/s^2

.

A.

0.5\,s

B.

2\,s

C.

1\,s

D.

3\,s

Question 40mcq

A ball is thrown upward in air. Compared with ideal motion, air resistance makes which relation most likely?

A.

t_{ascent}=t_{descent}

B.

t_{ascent}>t_{descent}

C.

t_{descent}=0

D.

t_{ascent}<t_{descent}