Maximum Height

Q. A rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6m/se{c}^2$. If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface would be

1. 490 m
2. 980 m
3. 245 m
4. 735 m

Q.

Two bodies are projected with the same velocity. If one is projected at an angle of ${30}^{\circ }$ and the other at an angle of ${60}^{\circ }$ to the horizontal, the ratio of the maximum heights reached is

1. 3 :1

2. 1 : 3

3. 2 : 1

4. 1 : 2

Q. A ball thrown by one player reaches the other in 2 sec. the maximum height attained by the ball above the point of projection will be about

1. 10 m
2. 7.5 m
3. 5 m
4. 2.5 m

Q.

If the initial velocity of a projectile be doubled, keeping the angle of projection same, the maximum height reached by it will

1. Remain the same

2. Be doubled

3. Be quadrupled

4. Be halved

Q.

If time of flight of a projectile is 10 seconds. Range is 500 meters. The maximum height attained by it will be

1. 125 m

2. 50 m

3. 100 m

4. 150 m

Q. A player kicks a football with an initial speed of $25{\text{ms}}^{-1}$ at an angle of ${45}^{\circ }$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? $(\text{Take}g=10{\text{ms}}^{-2})$

1. $h_{max}=10\text{m},T=2.5\text{s}$
2. $h_{max}=15.625\text{m},T=1.77\text{s}$
3. $h_{max}=15.625\text{m},T=3.54\text{s}$
4. $h_{max}=3.54\text{m},T=0.125\text{s}$

Q.

Two bodies are thrown up at angles of ${45}^{\circ }$ and ${60}^{\circ }$, respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is

1. $\sqrt{\frac{2}{3}}$

2. $\frac{2}{\sqrt{3}}$

3. $\frac{\sqrt{3}}{2}$

4. $\sqrt{\frac{3}{2}}$

Q. Give the formulae for the time period, maximum height reached and range of a projectile motion.

Q.

Two guns A and B can fire bullets at speeds $1\mathrm{km}{\sec }^{-1}$ and $2\mathrm{km}{\sec }^{-1}$ respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is :

1. $1:2$

2. $1:16$

3. $1:8$

4. $1:4$

Q. A body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at times $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is the acceleration due to gravity)

1. $\frac{g(t_1+t_2{)}^2}{4}$
2. $\frac{g(t_1+t_2{)}^2}{8}$
3. $\frac{g(t_2-t_1{)}^2}{4}$
4. $\frac{g(t_2-t_1{)}^2}{8}$

Q. Give the formulae for the time of flight, maximum height reached and range for a projectile motion.

Q.

1 parsec = _________ metres.

Q. If the initial velocity of a projectile be doubled. Keeping the angle of projection same, the maximum height reached by it will

1. Be doubled
2. Be quadrupled
3. Remain the same
4. Be halved

Q. A ball is thrown at different angles with the same speed u and from the same points and it has same range in both the cases. If $y_1$ and $y_2$ be the heights attained in the two cases, then $y_1+y_2=$

1. 
2. 
3. 
4. 

Q. A ball is projected with kinetic energy E at an angle of ${45}^{\circ }$ to the horizontal. At the highest point during its flight, its kinetic energy will be

1. $Zero$
2. $\frac{E}{2}$
3. $\frac{E}{\sqrt{2}}$
4. $E$

Q. The maximum height of a projectile for two complementary angles of projection is 50 m and 30 m respectively. The initial speed of projectile is

1. $10\sqrt{34}$ m/s
2. 20 m/s
3. 40 m/s
4. 10 m/s

Q. A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement time graph is characterised by

1. Negative slope and zero curvature
2. Zero slope and negative curvature
3. Zero slope and positive curvature
4. Positive slope and zero curvature

Q. A ball is projected from the ground with velocity $v$ such that its range is maximum. Match Column I entries with the correct entries in Column II.
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i.Velocity at half of the maximum height}& a.\sqrt{2}v\\ \text{ii.Velocity at the maximum height}& b.\sqrt{3}v/2\\ \text{iii. Change in velocity when its returns to the ground}& c.\frac{v}{\sqrt{2}}\\ \text{iv. Average velocity when its reaches the maximum height}& d.\frac{v}{2}\sqrt{\frac{5}{2}}\end{array}$

1. i – b ii – c iii – a iv – d
2. i – a ii – c iii – d iv – b
3. i – b ii – a iii – c iv – d
4. i – a ii – c iii –b iv – d

Q.

Two masses M1 and M2 are attached to the ends of a string which passes over a pulley attached to the top of an inclined plane. The angle of inclination of the plane in $\theta .Takeg=10m{s}^{-2}$.

1. 

2. 

3. 

4. 

Q.

Two equal masses (m) are projected at the same angle $\left(\theta \right)$ from two points separated by their range with equal velocities (v). The total momentum at the point of their collision is

1. 

2. 

3. 

4. 

Q.

In a projectile motion, velocity at maximum height is

1. $\frac{ucos\theta }{2}$

2. $ucos\theta$

3. $\frac{usin\theta }{2}$

4. None of these

Q. Two balls are thrown with the same speed but making complementary angle with the horizontal. If the angle of projection of one is ${60}^{\circ }$ and its maximum height is $h$, then the maximum height of the other will be

1. $4h$
2. $6h$
3. $\frac{h}{3}$
4. $2h$

Q. A boy throws a ball with an initial velocity and at an angle of elevation such that the range is $r$ and maximum height to which ball rises is $h$. Find the maximum range that can be obtained with same initial velocity.

1. $h+\frac{r^2}{8h}$
2. $2h+\frac{r^2}{8h}$
3. $2h-\frac{r^2}{8h}$
4. $h-\frac{r^2}{8h}$

Q. The position vector of a projectile is given by $\overrightarrow{r}=3t\hat{i}+(4t-5t^2)\hat{j}$. Find the ratio of maximum height and initial speed.
($g=10{\text{m/s}}^2$)

1. $\frac{4}{25}$
2. $\frac{4}{15}$
3. $\frac{8}{25}$
4. $\frac{8}{15}$

Q. If time of flight of a projectile is 10 seconds and range is $500m$. Then what will be the maximum height attained by it?
Take $g=10m/s^2$.

1. $125m$
2. $50m$
3. $100m$
4. $150m$

Q. A particle of mass $1kg$ is projected with velocity $20\sqrt{2}m{s}^{-1}\text{at}{45}^{\circ }$ with ground. Considering the moment when particle is at highest point, match the statements in Column -$1$ with results in Column-$2$
$(\text{Assume}g=10m/s^2)$

$\begin{array}{cc}\text{Column -1}& \text{Column -2}\\ \text{(A)Net torque on the particle}& \text{(P) 200 SI unit}\\ \text{about point of projection}& \\ \text{(B)Angular momentum of the}& \text{(Q) 400 SI unit}\\ \text{particle about point of}& \\ \text{projection}& \\ \text{(C)Angular velocity of the}& \text{(R)1.0 SI unit}\\ \text{particle about point of}& \\ \text{projection}& \\ & \text{(S)None}\end{array}$

1. $A-P,B-Q,C-R$
2. $A-Q,B-Q,C-S$
3. $A-Q,B-P,C-S$
4. $A-P,B-Q,C-S$

Q.

A ball is suspended by a thread of length l at the point O on the wall, forming a small angle $\beta (\beta >\alpha )$ with the vertical (see the figure). Then the thread with the ball was deviated through a small angle $\beta$ and set free. Assuming the collision of the ball against the wall to be perfectly elastic, the period of oscillation of this pendulum is:

1. $T=2\sqrt{\frac{l}{g}}[\frac{\pi }{2}+si{n}^{-1}\left(\frac{\alpha }{\beta }\right)]$
2. $T=2\pi \sqrt{\frac{l}{g}}[\frac{\pi }{2}+si{n}^{-1}\left(\frac{\alpha }{\beta }\right)]$
3. $T=2\pi \sqrt{\frac{l}{g}}[\frac{\pi }{2}+co{s}^{-1}\left(\frac{\alpha }{\beta }\right)]$
4. $T=2\sqrt{\frac{l}{g}}[\frac{\pi }{2}+co{s}^{-1}\left(\frac{\alpha }{\beta }\right)]$

Q.

In a projectile motion, velocity at maximum height is

1. $\frac{ucos\theta }{2}$

2. $ucos\theta$

3. $\frac{usin\theta }{2}$

4. None of these

Q.

A shot is fired at an angle to the horizontal such that it strikes the hill while moving horizontally. Find initial angle of projection.

1. 

2. 

3. 

4. none of these

Q. A particle moving with velocity of magnitude V change its direction of motion by angle $\theta$ without change in speed. Then the change in magnitude of velocity

1. $2Vsin\frac{\theta }{2}$
2. $2Vcos\frac{\theta }{2}$
3. $2Vsin\theta$
4. None of these