Range

Q.

Assertion: In javelin throw, the athlete throws the projectile at an angle of more than 45^∘.

Reason: The maximum range does not depend upon the angle of projection.

1. Both assertion and reason are the correct answer, reason is the correct explanation for assertion.

2. Both assertion and reason are correct. The answer reason is the incorrect explanation for the assertion.

3. The assertion is correct and the reason is incorrect.

4. Both assertion and reason are incorrect.

Q. Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long–jump event

1. Speed before he jumps and his weight
2. The direction in which he leaps and the initial speed
3. The force with which he pushes the ground and his speed
4. None of these

Q.

If the horizontal range of a projectile is equal to the maximum height reached, then the corresponding angle of projection is

1. ${\tan }^{-1}$$\left(1\right)$

2. ${\tan }^{-1}\left(\sqrt{3}\right)$

3. ${\tan }^{-1}\left(4\right)$

4. ${\tan }^{-1}\left(12\right)$

Q. The maximum range of a projectile is $22\text{m}$. When it is thrown at an angle of ${15}^{\circ }$ with the horizontal, its range will be-

1. $22\text{m}$
2. $6\text{m}$
3. $15\text{m}$
4. $11\text{m}$

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 $\theta$ < 45)

1. 2 : 1

2. 1 : 2

3. 1 : 1

4. 2 : 3

Q. The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

1. ${\tan }^{-1}\left(\frac{1}{4}\right)$
2. ${\tan }^{-1}\left(2\right)$
3. ${\tan }^{-1}\left(4\right)$
4. $\frac{\pi }{4}$

Q.

Distance between a frog and an insect on a horizontal plane is $9m$. Frog can jump with a maximum speed of $\sqrt{10}m/s$ . Minimum number of jumps required by the frog to catch the insect is (Take $g=10m/s^2$)

1. 7

2. 8

3. 9

4. 4

Q. The range of a projectile for a given initial velocity is maximum when the angle of projection is ${45}^{\circ }$. The range will be minimum, if the angle of projection is

1. ${90}^{\circ }$
2. ${180}^{\circ }$
3. ${60}^{\circ }$
4. ${75}^{\circ }$

Q.

A boy playing on the roof of a 10m high building throws a ball with a speed of 10 m/s at an angle of ${30}^{\circ }$ with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground $(g=10m/s^2,sin{30}^{\circ }=\frac{1}{2},cos{30}^{\circ }=\frac{\sqrt{3}}{2})$

1. 8.66 m

2. 5.20 m

3. 4.33 m

4. 2.60 m

Q. A player kicks a football at an angle of ${45}^{\circ }$ with a velocity of $30m{s}^{-1}$. A second player $120m$ away along the direction of kick starts running to receive the ball at that instant. Find the speed with which second player should run to reach the ball before it hits the ground $(g=10m{s}^{-2})$

1. $5\sqrt{2}m/s$
2. $4\sqrt{2}m/s$
3. $5m/s$
4. $10\sqrt{2}m/s$

Q.

A cannon on a level plain is aimed at an angle $\alpha$ above the horizontal and a shell is fired with a muzzle velocity $v_0$ towards a vertical cliff at a distance R away. Then the height from the bottom at which the shell strikes the side walls of the cliff is

1. $Rsin\alpha -\frac{g{R}^2}{2v_0^{2}si{n}^2\alpha }$

2. $Rcos\alpha -\frac{g{R}^2}{2v_0^{2}co{s}^2\alpha }$

3. $Rtan\alpha -\frac{g{R}^2}{2v_0^{2}co{s}^2\alpha }$

4. $Rtan\alpha -\frac{g{R}^2}{2v_0^{2}si{n}^2\alpha }$

Q. A particle is projected with a velocity $v$ such that its range on horizontal plane is twice the greatest height attained by it. The range of the projectile will be ($g$ is the acceleration due to gravity).

1. $\frac{4v^2}{5g}$
2. $\frac{4g}{5v^2}$
3. $\frac{v^2}{g}$
4. $\frac{4v^2}{\sqrt{5}g}$

Q.

A ball is thrown from a point with a speed $v_0$ at an angle of projection $\theta$. From the same point and at the same instant a person starts running with a constant speed $\frac{v_0}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection

1. $Yes,{60}^{\circ }$

2. $Yes,{30}^{\circ }$

3. $No$

4. $Yes,{45}^{\circ }$

Q. If a body A of mass M is thrown with velocity V at an angle of ${30}^{\circ }$ to the horizontal and another body B of the same mass is thrown with the same speed at an angle of ${60}^{\circ }$ to the horizontal. The ratio of horizontal range of A to B will be

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

Q. A person wishes to hit target from a tower of height 32 m by throwing a projectile at 10 m/s aiming directly to it as shown in figure. How short from target will the projectile fall? ($g=10m/s^2$)Write until two digits after the decimal point.

Q.

A particle covers 50 m distance when projected with an initial speed. On the same surface it will cover a distance, when projected with double the initial speed

1. 100 m

2. 150 m

3. 200 m

4. 250 m

Q. If a body A of mass M is thrown with velocity V at an angle of ${30}^{\circ }$ to the horizontal and another body B of the same mass is thrown with the same speed at an angle of ${60}^{\circ }$ to the horizontal. The ratio of horizontal range of A to B will be

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

Q. If two bodies are projected at ${30}^{\circ }$ and ${60}^{\circ }$ respectively, with the same velocity, then

1. Their ranges are same
2. Their heights are same
3. Their times of flight are same
4. All of these

Q.

A bullet is fired from a cannon with velocity 500 m/s. If the angle of projection is ${15}^{\circ }$ and $g=10m/s^2$. Then the range is

1. $25\times {10}^{3}m$

2. $12.5\times {10}^{3}m$

3. $50\times {10}^{2}m$

4. $25\times {10}^{2}m$

Q. The maximum range of a projectile is $22\text{m}$. When it is thrown at an angle of ${15}^{\circ }$ with the horizontal, its range will be-

1. $22\text{m}$
2. $6\text{m}$
3. $15\text{m}$
4. $11\text{m}$

Q.

An aeroplane moving horizontally with a speed of 720 km/h drops a food pocket, while flying at a height of 396.9 m. the time taken by a food pocket to reach the ground and its horizontal range is (Take g = 9.8 m/$se{c}^2$)

1. 3 sec and 2000 m

2. 5 sec and 500 m

3. 8 sec and 1500 m

4. 9 sec and 1800 m