Throwing and Catching at Same Height

Q.

A stone falls freely under gravity. It covers distances h_1, h_2, h₃ in the first 5 seconds , the next 5 seconds and the next 5 seconds respectively. What is the relation between h_1, h₂ and h_{3 .}

Q.

A body dropped from top of a tower fall through 40m during the last two seconds of its fall. The height of the tower is (g=10m/s^{​​​​​​2}).

A) 60m

B) 45m

C) 80m

D) 50m

Q.

A body is thrown vertically upward with velocity $u$, the greatest height $h$ to which it will rise is

1. $\frac{u^{}}{g}$

2. $\frac{u^2}{2g}$

3. $\frac{u^2}{g}$

4. $\frac{u^{}}{2g}$

Q.

A balloon is ascending at the rate of 9.8m/s. At height of 39.2m above the ground. When a foot packet is dropped from balloon. After how much time and with what velocity does it reach the ground. ($g=9.8m/s^2$)

Q. When a ball is thrown vertically upwards with velocity $v_0$, it reaches a maximum height of $h$. If one wishes to triple the maximum height then the ball should be thrown with velocity.

1. $\sqrt{3}{v}_0$
2. $3v_0$
3. $\frac{3}{2}{v}_0$
4. $9v_0$

Q. A body is thrown vertically upward from the top $A$ of tower. It reaches the ground in $t_{1}s$. If it is thrown vertically downwards from $A$ with the same speed it reaches the ground in $t_{2}s$. If it is allowed to fall freely from $A$, then the time it takes to reach the ground is given by

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

Q. A man can swim with speed of $4\text{kmph}$ in still water. He crosses $1\text{km}$ wide river making strokes normal to river current. The river flows steadily at $3\text{kmph}$. How far down the river, he drifts when he reaches the other bank?

1. $500\text{m}$

2. $600\text{m}$

3. $750\text{m}$
4. $1000\text{m}$

Q.

A $0.5kg$ ball is thrown up with an initial speed $14m{s}^{-1}$ and reaches a maximum height of $8.0m$. How much energy is dissipated by air drag acting on the ball during the ascent?

1. $19.6Joule$

2. $4.9Joule$

3. $10Joule$

4. $9.8Joule$

Q.

Two particles are released from the same height at an interval of 1 second how long after the first particle begins to fall will the two partocles be 10 m apart

Q. A ball is thrown vertically downward with a velocity $u$ from the top of a tower. It strikes the ground with a velocity $5u$. The time taken by the ball to reach the ground is given by

1. $2.5u$
2. $\frac{2u}{g}$
3. $\frac{4u}{g}$
4. $5u$

Q.

A piece of wood of mass $0.03kg$ is dropped from the top of a building $100m$ high. At the same time, a bullet of mass $0.02kg$ is fired vertically upward with a velocity of $100m{s}^{-1}$ from the ground the bullet gets embedded in the wooded piece after striking. Then the maximum height to which the combined system reaches above the building before falling below is: ( take $g=10m{s}^{-2}$ ).

1. $40$

2. $30$

3. $20$

4. $10$

Q.

State the SI unit of acceleration due to gravity.

Q. A stone dropped is from the top of a building and One second later another stone is thrown down with velocity 20m/s.how far below the top will the second over take the first?

Q. A body is projected up with a speed 'u' and the time taken by it is T to reach the maximum height H . Pick out the correct statement

1. It acquires velocity U/2 in T/2 sec
2. Its velocity is U/2 at H/2 sec
3. It reaches H/2 in T/2 sec
4. Same velocity at 2T

Q. A stone is thrown vertically upward with an initial velocity $v_o.$ The distance travelled in time $\frac{1.5v_o}{g}$ is

1. $\frac{v_o^2}{2g}$
2. $\frac{3v_o^2}{8g}$
3. $\frac{5v_o^2}{8g}$
4. None of these

Q. A person throws vertically $n$ 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. $\frac{g}{n^2}$
2. $2g{n}^2$
3. $2gn$
4. $\frac{g}{2n^2}$

Q. A ball is projected upwards from the foot of a tower. The ball crosses the top of the tower twice after an interval of $6\text{s}$ and the ball reaches the ground after $12\text{s}$. The height of the tower is ($g=10m/s^2$)

1. $120\text{m}$
2. $80\text{m}$
3. $135\text{m}$
4. $175\text{m}$

Q.

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s .what is the amount of gas ejected per second to supply the needed thrust and to give an upward acceleration of 20 m/s²

Q. From the top of a tower, a particle is thrown vertically downwards with a velocity of $10m/s$. The ratio of distances covered by it in the $3^{rd}$ and $2^{nd}$ seconds of its motion is (Take $g=10m/s^2$)

1. $5:7$
2. $7:5$
3. $3:5$
4. $6:3$

Q. A boy projects a stone vertically perpendicular to the trolley car with a speed $v$. If the trolley car moves with a constant velocity $u$, the time of flight of the stone is:

1. $\frac{2v}{g}$
2. $\frac{u+v^2}{g}$
3. none of these
4. $\frac{2u}{g}$

Q. A ball is thrown vertically upward from the top of a tower. Velocity at depth $h$ from the point of projection is twice of the velocity at height $h$ above the point of projection. Find the maximum height reached by the ball.

1. $3h$
2. $2h$
3. $\left(\frac{5}{3}\right)h$
4. $\left(\frac{4}{3}\right)h$

Q.

A train $240m$ long passes a pole in $24sec$. How long will it take to pass a platform which is $650m$ long?

1. $65$ $sec$

2. $89$ $sec$

3. $100$ $sec$

4. $150$ $sec$

Q. A uniform rod of length $l$ is pivoted at point $A$. It is struck by a horizontal force which delivers an impulse $J$ at a distance $x$ from point $A$ as shown in the figure, impulse delivered by pivot is zero if $x$ is equal to

1. $l/3$
2. $3l/4$
3. $l/2$
4. $2l/3$

Q. A particle is projected upwards from top of a tower of height $40m$ with a speed of $10m/s$. The time it will take to strike ground $(g=10m/s^2)$ will be

1. $1s$
2. $2s$
3. $3s$
4. $4s$

Q. A person throws balls into air after every second. The next ball is thrown when the velocity of the first ball is zero. How high do the ball rise above his hand?

1. $2m$
2. $10m$
3. $5m$
4. $8m$

Q. A stone is thrown vertically upward with an initial velocity $v_o$. The distance travelled in time $\frac{4v_o}{3g}$ is

1. $\frac{v_o^2}{2g}$
2. $\frac{3v_o^2}{8g}$
3. $\frac{4v_o^2}{9g}$
4. $\frac{5v_o^2}{9g}$

Q.

How can acceleration be negative?

Q. A ball is projected upwards from the top of a tower of height $40m$ with a speed of $10m/s$, The time it will take to strike the ground $(g=10m/s^2)$ will be

1. 1 s
2. 2 s
3. 3 s
4. 4 s

Q.

A ball thrown vertically upwards falls back on the ground after $6\mathrm{s}$, Assuming that the equation of motion is of the form $\mathrm{s}=\mathrm{ut}–4.9{\mathrm{t}}^2$, where$\mathrm{s}$ is in meter and $\mathrm{t}$ is in second, find the velocity at $\mathrm{t}=0$

1. $0\mathrm{m}/\mathrm{s}$

2. $1\mathrm{m}/\mathrm{s}$

3. $29.4\mathrm{m}/\mathrm{s}$

4. $\mathrm{None}\mathrm{of}\mathrm{these}$

Q. A solid sphere of radius $R$ starts rotating on rough horizontal surface with translational velocity $V_0$ and initial angular velocity ${\omega }_0=\frac{2V_0}{3R}$ . The sphere starts pure rolling after some time $t$. if $V$ is the translational velocity at pure rolling. Assume uniformly accelerated motion up to start of pure rolling:
if $S$ is the distance covered by the sphere in rotational motion up to the instant at which pure rolling starts, find the velocity (translational) of the sphere during the pure rolling

1. $\frac{33}{38}\frac{S}{t}$
2. $\frac{31}{38}\frac{S}{t}$
3. $\frac{38}{33}\frac{S}{t}$
4. $\frac{37}{38}\frac{S}{t}$