Throwing and Catching at Same Height

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

Q.

What is the acceleration of the ball at the highest point?

1. 0 m/s²

2. 9.8 m/s²

3. -9.8 m/s²

4. none of these

Q.

What is the acceleration of the ball at the highest point?

1. 0 m/s²

2. 9.8 m/s²

3. -9.8 m/s²

4. none of these

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.

Does the Gravity have constant acceleration?

Q. At time $t=0$, a bullet is fired vertically upwards with a speed of 98 $m{s}^{-1}.$ At time $t=5s$ (i.e., 5 seconds later) a second bullet is fired vertically upwards with the same speed. If the air resistance is neglected, which of the following statements is/are true?

1. The two bullets will be at the same height above the ground at $t=12.5s$.
2. The two bullets will reach back their starting points at the same time.
3. The two bullets will have the same speed at $t=20sec$.
4. The two bullets will attain the same maximum height.

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

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

Q.

A body projected vertically upwards takes 3 seconds to reach the highest point. Calculate the velocity with which it was projected, .$g=9.8\frac{m}{s^2}.$

Q. A ball is thrown vertically upward from the top of a cliff. Take the starting position of motion as origin and upward direction as positive. Column I specifies the position, velocity and /or acceleration of the particle at any instant. Column II given their signs $(+)$ or $(-)$ at that moment. Match the columns
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i.When the ball is above the point}& \text{a. always positive}\\ \text{of projection, its displacement is}& \\ \text{ii. When the ball is above the point}& \text{b. always negative}\\ \text{of projection, its velocity is}& \\ \text{iii. When the ball is above the point}& \text{c. May be positive or may be}\\ \text{of projection, its acceleration is}& \text{negative}\\ \text{iv.When the ball is below the point}& \text{d. may be zero}\\ \text{of projection, its acceleration is}& \end{array}$

1. $i.\to c,ii.\to b,iii.\to a,iv.\to b.$
2. $i.\to a.,ii.\to c.,iii.\to a,iv.\to d.$
3. $i.\to a.,ii.\to c.,iii.\to b.,iv.\to b.$
4. $i.\to b,ii.\to c.,iii.\to a,iv.\to b.$

Q. A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (Given g=9.8$m/s^2$)

1. At least 0.8 m/s
2. Any speed less than 19.6 m/s
3. Only with speed 19.6 m/s
4. More than 19.6 m/s

Q. When a ball is thrown vertically upwards with velocity $v_0$, it reaches a maximum height of $h$. With what velocity should the ball be thrown to reach half the maximum height.

1. $\sqrt{2}{v}_0$
2. $\sqrt{0.5}{v}_0$
3. $\sqrt{1.5}{v}_0$
4. $\sqrt{3}{v}_0$

Q. A body A is projected upwards with a velocity of $98\frac{m}{s}$. The second body B is projected upwards with the same initial velocity but after 4 sec. Both the bodies will meet after

1. 6 sec
2. 8 sec
3. 10 sec
4. 12 sec

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 $6s$ and the ball reaches the ground after $12s$. The height of the tower is $(g=10m/s^2)$

1. $120m$
2. $135m$
3. $175m$
4. $80m$

Q.

A car falls off a ledge and drops to the ground in $0.5s$. How high is the ledge from the ground?

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 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 reaches $\frac{H}{2}$ in $\frac{T}{2}$ sec
2. It acquires velocity $\frac{U}{2}$ in $\frac{T}{2}$ sec
3. Its velocity is $\frac{U}{2}$ at $\frac{H}{2}$ sec
4. Same velocity at 2T

Q. A particle is thrown vertically upwards. If its velocity at half of the maximum height is $10\frac{m}{s}$, then maximum height attained by it is (Take $g=10\frac{m}{s^2}$)

1. $15m$
2. $20m$
3. $10m$
4. $5m$

Q.

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is

1. Equal to the time of fall

2. Less than the time of fall

3. Greater than the time of fall

4. Twice the time of fall

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