Motion Under Gravity

Q. A juggler is juggling $7$ balls simultaneously. If the time gap to pass ball from one hand to the other is $2$ second then find the maximum height attained by each ball.

1. $100\text{m}$
2. $120\text{m}$
3. $180\text{m}$
4. $200\text{m}$

Q. A body is projected up with a velocity equal to ${\left(\frac{3}{4}\right)}^{th}$ of the escape velocity from the surface of the earth. The height it reaches is (Radius of earth $=R$)

1. $\frac{10R}{3}$
2. $\frac{9}{7}R$
3. $\frac{9}{8}R$
4. $\frac{10R}{9}$

Q. A body travels half of its total path in the last second of its fall from rest. If $t$ and $H$ are the time and height of its fall (take $g=10{\text{m/s}}^2$). Then,

1. $t=2.4\text{s}$
2. $t=3.4\text{s}$
3. $H=28.8\text{m}$
4. $H=58.3\text{m}$

Q. A stone is thrown vertically upwards with an initial velocity of $30\text{m/s}$. The time taken for the stone to rise to its maximum height is
[Take $g=10{\text{m/s}}^2$]

1. $4\text{sec}$
2. $2\text{sec}$
3. $3\text{sec}$
4. $6\text{sec}$

Q. A particle is falling freely under gravity. If in the first $t$ seconds, it covers distance $x_1$ and in the next $t$ seconds, it covers distance $x_2$, then $t$ is given by

1. $\sqrt{\frac{x_2-x_1}{g}}$
2. $\sqrt{\frac{x_2+x_1}{g}}$
3. $\frac{\sqrt{2(x_2-x_1)}}{g}$
4. $\frac{\sqrt{2(x_2+x_1)}}{g}$

Q. A ball is tossed up with an initial speed of $24\text{m/s}$. How high up will it go?

1. $29.4\text{m}$
2. $30.2\text{m}$
3. $32.4\text{m}$
4. $34.6\text{m}$

Q. A ball is thrown upward from the top of a tower of height $50\text{m}$ with a velocity of $15\text{m/s}$. Find the time when it strikes the ground. Take $g=10\text{m}/s^2$.

1. $2\text{s}$
2. $3\text{s}$
3. $4\text{s}$
4. $5\text{s}$

Q. A person throws vertically $10$ balls per second with the same velocity. He throws a ball whenever the previous one is at its highest point. The height to which the balls rise is

1. $10\text{m}$
2. $5\text{m}$
3. $5\text{cm}$
4. $10\text{cm}$

Q. From the top of a tower, a stone is thrown up and reaches the ground in time $t_1$ . A second stone is thrown down with the same speed and reaches the ground in time $t_2$. A third stone is released from rest and reaches the ground in time $t_3$ -

1. $t_3=\frac{1}{2}(t_1+t_2)$
2. $t_3=\sqrt{t_1{t}_2}$
3. $\frac{1}{t_3}=\frac{1}{t_2}-\frac{1}{t_1}$
4. $t_3^2=t_1^2-t_2^2$

Q. A ball is thrown vertically upward with a velocity of $10\text{m/s}$ from the top of a tower of height of $50\text{m}$. Find the time taken by the ball to reach a height $10\text{m}$ from the ground. (Take $g=10{\text{m/s}}^2$)

1. $1\text{s}$
2. $3\text{s}$
3. $4\text{s}$
4. $5\text{s}$

Q. A person standing near the edge of the top of a building throws two balls $A$ and $B$. The ball $A$ is thrown vertically upwards and $B$ is thrown vertically downward with the same speed. The ball $A$ hits the ground with a speed $v_A$ and the ball $B$ hits the ground with a speed $v_B$. Then,

1. $v_A>v_B$
2. $v_A<v_B$
3. $v_A=v_B$
4. The relation between $v_A$ and $v_B$ depends on height of the building above the ground.

Q. A particle is thrown up with velocity $20\text{m/s}$. Find the time when velocity is $10\text{m/s}$.
[Take $g=10{\text{m/s}}^2$]

1. $1\text{sec}$
2. $2\text{sec}$
3. $3\text{sec}$
4. $\text{Both (a) and (c)}$

Q. A stone dropped from a certain height reaches ground in $5\text{sec}$. If it is dropped and stopped for infinitesimal time interval at $t=3\text{s}$, then time taken by the stone to reach the ground is

1. $6\text{s}$
2. $6.5\text{s}$
3. $7\text{s}$
4. $7.5\text{s}$

Q. A stone thrown upward with a speed $u$ from the top of the tower reaches the ground with a velocity $3u$. The height of the tower is

1. $3u^2/g$
2. $6u^2/g$
3. $4u^2/g$
4. $9u^2/g$

Q. A stone is dropped from $25\text{th}$ storey of a multistorey building and reaches the ground in $5\text{s}$. How many storey of the building will the stone cover in first second, if the height of each storey is same?
(Take $g=10m/s^2$)

1. $1$
2. $2$
3. $3$
4. $5$

Q. A stone is dropped into water from a bridge $44.1\text{m}$ above the water. Another stone is thrown vertically downward $1\text{sec}$ later. Both strike the water simultaneously. What was the initial speed of the second stone.

1. $12.25\text{m/s}$
2. $14.75\text{m/s}$
3. $16.23\text{m/s}$
4. $17.15\text{m/s}$

Q. Two bodies are projected vertically upwards from one point with the same initial velocities $v_{0}m/s$. The second body is thrown $\tau s$ after the first. The two bodies meet after time

1. $\frac{v_0}{g}-\frac{\tau }{2}$
2. $\frac{v_0}{g}+\tau$
3. $\frac{v_0}{g}+\frac{\tau }{2}$
4. $\frac{v_0}{2g}-\tau$

Q. A particle is released from rest from a tower of height $3h$. The ratio of times to fall equal heights $h$ i.e., $t_1:t_2:t_3$ is

1. $\sqrt{3}:\sqrt{2}:1$
2. $3:2:1$
3. $9:4:1$
4. $1:(\sqrt{2}-1):(\sqrt{3}-\sqrt{2})$

Q. A body is thrown upwards and reaches half of its maximum height. At that position

1. its acceleration is minimum.
2. its velocity is maximum.
3. its velocity is zero.
4. its acceleration is constant.

Q. A stone dropped from a building of height $h$ and it reaches the ground after $t$ seconds. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity $u$ and they reach the ground after $t_1$ and $t_2$ seconds respectively, then

1. $t=t_1-t_2$
2. $t=\frac{t_1+t_2}{2}$
3. $t=\sqrt{t_1{t}_2}$
4. $t=t_1^2{t}_2^2$

Q. A ball is projected vertically up with a velocity of $20m{s}^{-1}$. Its velocity at the height of $15\text{m}$ is
(Take $g=10m{s}^{-2})$

1. $10m{s}^{-1}$
2. $15m{s}^{-1}$
3. $-10m{s}^{-1}$
4. $\text{Both a and c}$

Q. From the top of a tower, a stone is thrown up and reaches the ground in time $t_1$ . A second stone is thrown down with the same speed and reaches the ground in time $t_2$. A third stone is released from rest and reaches the ground in time $t_3$ -

1. $t_3=\frac{1}{2}(t_1+t_2)$
2. $t_3=\sqrt{t_1{t}_2}$
3. $\frac{1}{t_3}=\frac{1}{t_2}-\frac{1}{t_1}$
4. $t_3^2=t_1^2-t_2^2$

Q.

So it takes $\frac{u}{g}$secs to go up, how long will it take to come down?(as mentioned there is no air)

1. longer than $\frac{v}{g}$

2. shorter than $\frac{v}{g}$ because in the previous case gravity is acting against velocity and here it is acting along the velocity

3. equal to $\frac{v}{g}$

4. I don't know

Q. A wooden block of mass $20g$ is dropped from the top of the cliff $50m$ high. Simultaneously a bullet of mass $20g$ is fired from the foot of the cliff upwards with a velocity $25m{s}^{-1}$. The bullet and the wooden block will meet each other at a distance from top of the cliff : ($g=10m{s}^{-2}$)

1. $10m$
2. $20m$
3. $30m$
4. $40m$

Q. A ball is dropped from a bridge $122.5\text{m}$ high. After the first ball has fallen for $2$ second, a second ball is thrown straight down after it, what must be the initial velocity of the second ball, so that both the balls hit the surface of water at the same time?

1. $26.1\text{m/s}$
2. $9.8\text{m/s}$
3. $55.5\text{m/s}$
4. $49\text{m/s}$

Q.

A ball is dropped from the top of a building at $t=0$. At a later time $t=t_0$, a second ball is thrown downward with an initial speed $v_0$. Obtain an expression for the time t at which the two balls meet.

1. $\left[\frac{v_0-\frac{g{t}_0}{2}}{v_0-g{t}_0}\right]t_0$

2. $\left[\frac{v_0+\frac{g{t}_0}{2}}{v_0-g{t}_0}\right]t_0$

3. $\left[\frac{v_0-\frac{g{t}_0}{2}}{v_0+g{t}_0}\right]t_0$

4. $\left[\frac{v_0+\frac{g{t}_0}{2}}{v_0+g{t}_0}\right]t_0$

Q. An object is dropped from rest from a large height. Assume $g$ to be constant throughout the motion. The time taken by it to fall through successive distances of $1\text{m}$ each will be

1. same, which is $\sqrt{\frac{2}{8}}$ seconds
2. in the ratio of the square roots of the integers 1, 2, 3, …
3. in the ratio of the difference in the square roots of the integers, i.e., $\sqrt{1},(\sqrt{2}-\sqrt{1}),(\sqrt{3}-\sqrt{2}),(\sqrt{4}-\sqrt{3})$, ...
4. in the ratio of the reciprocals of the square roots of the integers, i.e., $\frac{1}{\sqrt{1}},\frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},$ ...

Q. A ball is thrown upward from the edge of a cliff with an initial velocity of $8\text{m/s}$. How fast will it go at $0.5\text{sec}$ later.
[Take $g=10{\text{m/s}}^2$]

1. $2\text{m/s}$
2. $3\text{m/s}$
3. $4\text{m/s}$
4. $1\text{m/s}$

Q. A hot air balloon is rising vertically upwards at a constant velocity of $10{\text{ms}}^{-1}$. When it is at a height of $45\text{m}$ from the ground, a man bails out from it. After $3\text{s}$ he opens his parachute and decelerates at a constant rate of $5{\text{ms}}^{-2}$. After how long does the parachutist takes to hit the ground after his exit from the balloon?

1. $4\text{s}$
2. $5\text{s}$
3. $6\text{s}$
4. $7\text{s}$

Q. A ball is released from height $h$ and another ball from height $2h$. The ratio of time taken by the two balls to reach the ground is

1. $1:\sqrt{2}$
2. $\sqrt{2}:1$
3. $2:1$
4. $1:2$