Maximum Range

Q. A large number of bullets are fired in all directions with same speed v. What is the maximum area on the ground on which these bullets will spread

1. $\pi \frac{v^2}{g}$
2. $\pi \frac{v^4}{g^2}$
3. ${\pi }^2\frac{v^4}{g^2}$
4. ${\pi }^2\frac{v^2}{g^2}$

Q. Galileo writes that for angles of projection of a projectile at angles $(45+\theta )and(45-\theta )$, the horizontal ranges described by the projectile are in the ratio of $(if\theta \le 45)$

1. 1 : 2
2. 2 : 1
3. 2 : 3
4. 1 : 1

Q.

A cricketer can throw a ball to a maximum horizontal distance of 100 m. The speed with which he throws the ball is (to the nearest integer)

1. $30m{s}^{-1}$

2. $42m{s}^{-1}$

3. $32m{s}^{-1}$

4. $35m{s}^{-1}$

Q.

For a given velocity, a projectile has the same range R for two angles of projection, if $t_{1}and{t}_2$ are the times of flight in the two cases then

1. 

2. 

3. 

4. 

Q. A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is

1. 100 m
2. 80 m
3. 60 m
4. 50 m

Q. A shell is fired from a gun from the bottom of a hill along its slope. The slope of the hill is $\alpha ={30}^{\circ }$, , and the angle of the barrel to the horizontal $\beta ={60}^{\circ }$. The initial velocity v of the shell is 21 m/sec. Then distance of point from the gun at which shell will fall

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

Q. The range of a particle when launched at an angle of ${15}^{\circ }$ with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of ${45}^{\circ }$ to the horizontal

1. 6.0 km
2. 0.75 km
3. 1.5 km
4. 3.0 km

Q. The maximum range of rifle bullet on the horizontal ground is 6 km its maximum range on an inclined of ${30}^{\circ }$ will be

1. 1 km
2. 2 km
3. 4 km
4. 6 km

Q. A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is

1. ${25}^{\circ }{8}^{\prime }$
2. ${33}^{\circ }{7}^{\prime }$
3. ${42}^{\circ }{8}^{\prime }$
4. ${53}^{\circ }{8}^{\prime }$

Q. The horizontal range of projectile fired at ${75}^{\circ }$ is $R$. If it is fired with same speed at ${45}^{\circ }$, what would be its range?

1. $\frac{R}{2}$
2. $\frac{2R}{3}$
3. $2R$
4. $\frac{R}{3}$

Q. Two guns $A$ and $B$ can fire bullets at speeds $1\text{km/s}$ and $2\text{km/s}$ respectively, 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. $1:16$
2. $1:2$
3. $1:4$
4. $1:8$

Q. The range of a particle when launched at an angle of ${15}^{\circ }$ with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of ${45}^{\circ }$ to the horizontal

1. 1.5 km
2. 3.0 km
3. 6.0 km
4. 0.75 km

Q. Two particles A and B are projected simultaneously in the direction shown in the figure with velocities $v_A=20m/s$ and $v_B=10m/s$ respectively. They collide in air after $\frac{1}{2}$ sec. Then

1. the angle $\theta$ is ${60}^{\circ }$
2. the distance $x$ is $5\sqrt{3}m$
3. the angle $\theta$ is ${30}^{\circ }$
4. the distance $x$ is $15\sqrt{3}m$

Q. A man fires a large number of bullets in all directions with same speed $\upsilon$. The maximum area on the ground on which these bullets will spread is :

1. $\frac{\pi v^2}{g}$
2. $\frac{v^2}{g^2}$
3. $\frac{\pi v^4}{g^2}$
4. $\frac{v^4}{g^2}$

Q.

A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. What is the maximum height attained by the ball?

1. 50 m

2. 60 m

3. 70 m

4. 80 m

Q. A particle is projected down on inclined plane with a velocity of $21m/s$ at an angle of ${60}^o$ with the horizontal. Its range on the inclined plane, inclined at an angle of ${30}^o$ with the horizontal is

1. $21dm$
2. $30dm$
3. $2.1dm$
4. $6dm$

Q. A lead bullet (specific beat = $0.032cal/g^{\circ }C$) is completely stopped when it strikes a target with a velocity of $300m/s$. The heat generated is equally shared by the bullet and the target.The rise in temperature of bullet will be.

1. ${16.7}^{o}C$
2. ${1.67}^{o}C$
3. ${167.4}^{o}C$
4. $267.4^{o}C$

Q. The range of a projectile when launched at angle $\theta$ is same as when launched at angle $2\theta$. What is the value of $\theta$?

1. ${30}^o$
2. ${45}^o$
3. ${60}^o$
4. ${15}^o$

Q. The range of projectile when launched at an angle of ${15}^{\circ }$ with the horizontal is $1.5km$. What is the range of the projectile when launched at an angle ${45}^{\circ }$ to the horizontal

1. $1.5km$
2. $0.75km$
3. $3.0km$
4. $6.3km$

Q. A boy throws a ball upwards at ${60}^o$ to the horizontal with a speed of $80m/s$ and it reaches the maximum height $H$ , If he throws the same ball vertically downward from a height of $H$ with initial speed of $40m/s$ , The ball will reach ground with speed nearly:

1. $48m/s$
2. $56m/s$
3. $64m/s$
4. $80m/s$

Q. A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is

1. ${25}^{\circ }{8}^{\prime }$
2. ${33}^{\circ }{7}^{\prime }$
3. ${42}^{\circ }{8}^{\prime }$
4. ${53}^{\circ }{8}^{\prime }$

Q. Two balls are thrown simultaneously at two different angles with the same speed $v_o$ from the same position so that both have equal ranges. If $H_1$ and $H_2$ be the maximum heights attained in the two cases, then the sum $H_1+H_2$ is equal to

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

Q.

The maximum range of a gun on horizontal terrain is 16 km. If $g=10m/s^2$. What must be the muzzle velocity of the shell

1. 200 m/s

2. 400 m/s

3. 100 m/s

4. 50 m/s

Q. A ball is projected from a point in a horizontal plane so as to strike a vertical wall at right angle and after rebounding from the wall and once from the horizontal plane it returns to the point of projection. Find coefficient of restitution (e) for the two collisions, assuming it to be same for both collision. Find the value of 1/e.

Q.

A cricketer can throw a ball to a maximum horizontal distance of 100 m. The speed with which he throws the ball is (to the nearest integer)

1. $30m{s}^{-1}$

2. $42m{s}^{-1}$

3. $32m{s}^{-1}$

4. $35m{s}^{-1}$

Q. A projectile of mass $m$ is fired with velocity $u$ making angle $\theta$ with the horizontal. Its angular momentum about the point of projection when it hits the ground is given by

1. $\frac{2mu{\sin }^2\theta \cos \theta }{g}$
2. $\frac{2m{u}^3{\sin }^2\theta \cos \theta }{g}$
3. $\frac{m{u}^3{\sin }^2\theta \cos \theta }{2g}$
4. $\frac{mu{\sin }^2\theta \cos \theta }{2g}$

Q. A shell is fired from a gun from the bottom of a hill along its slope. The slope of the hill is $\alpha ={30}^{\circ }$, , and the angle of the barrel to the horizontal $\beta ={60}^{\circ }$. The initial velocity v of the shell is 21 m/sec. Then distance of point from the gun at which shell will fall

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

Q. A truck is moving horizontally with velocity $v$. A ball thrown vertically upward with a velocity $u$ at angle $\theta$ to the horizontal from the truck relative to it. The horizontal range of the ball relative to the ground is

1. $\frac{2\times (v+u\cos \theta )u\sin \theta }{g}$
2. $\frac{2\times (v+u\sin \theta )u\cos \theta }{g}$
3. $\frac{2\times (v-u\cos \theta )u\sin \theta }{g}$
4. $\frac{2\times (v-u\sin \theta )u\cos \theta }{g}$

Q. If a body is projected with a velocity of $9.8m/s$ making an angle of ${45}^o$ with the horizontal, then the range of the projectile is (Take $g=9.8m/s^2$)

1. $39.2m$
2. $4.9m$
3. $19.6m$
4. $9.8m$

Q. A gun is aimed at a horizontal target. It takes $\frac{1}{2}s$ for the bullet to reach the target. The bullet hits the target $x$ meter below the aim. Then $x$ is equal to (Take $g=9.8m/s^2$)

1. $\frac{9.8}{4}m$
2. $\frac{9.8}{8}m$
3. $9.8m$
4. $19.6m$