A projectile thrown with a speed \(v\) at an angle \(θ\) has a range \(R\) on the surface of the Earth. For same \(v\) and \(θ\), its range on the surface of the Moon will be \(\left(\text{acceleration due to gravity on moon}=\dfrac g6\right)\):

1. \(R/6\)

2. \(6 R\)

3. \(R/36\)

4. \(36 R\)

A ball is projected with kinetic energy \(E\) at an angle of \(45^°\) to the horizontal. At the highest point during its flight, its kinetic energy will be:

1. Zero

2. \(\dfrac E2\)

3. \(\dfrac E{\sqrt2}\)

4. \(E\)

At the top of the trajectory of a projectile, the magnitude of the acceleration is:

1. Maximum

2. Minimum

3. Zero

4. \(g\)

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

1. \(25^\circ 8 '\)

2. \(33^\circ 7 '\)

3. \(42^\circ 8 '\)

4. \(53^\circ 8 '\)

Two bodies are projected with the same velocity. If one is projected at an angle of \(30^°\) and the other at an angle of \(60^°\) to the horizontal, the ratio of the maximum heights reached is:

1. \(3 : 1\)

2. \(1 : 3\)

3. \(1 : 2\)

4.  \( 2 : 1\)

If the range of a gun that fires a shell with muzzle speed v is R, then the angle of elevation of the gun is 

(1) ${\cos }^{-1}\left(\frac{{\displaystyle v^2}}{{\displaystyle Rg}}\right)$

(2) ${\cos }^{-1}\left(\frac{{\displaystyle gR}}{{\displaystyle v^2}}\right)$

(3) $\frac{1}{2}\left(\frac{{\displaystyle v^2}}{{\displaystyle Rg}}\right)$

(4) $\frac{1}{2}{\sin }^{-1}\left(\frac{{\displaystyle gR}}{{\displaystyle v^2}}\right)$

If a body \(A\) of mass \(M\) is thrown with a velocity \(v\) at an angle of \(30^°\) to the horizontal and another body \(B\) of the same mass is thrown with the same speed at an angle of \(60^°\) to the horizontal. The ratio of the horizontal range of \(A\) to \(B\) will be:

1. \(1 : 3\)

2. \(1 : 1\)

3. \(1 : \sqrt3\)

4. \( \sqrt3:1\)

Four bodies \(P\), \(Q\), \(R\) and \(S\) are projected with equal velocities having angles of projection \(15^{\circ},\) \(30^{\circ},\)\(45^{\circ},\) and \(60^{\circ}\) with the horizontal respectively. The body having the shortest range is? 

A stone projected with a velocity \(u\) at an angle \(\theta\) with the horizontal reaches maximum height \(H_1.\) When it is projected with velocity \(u\) at an angle \(\left(\frac{\pi}{2}-\theta\right)\) with the horizontal, it reaches maximum height \(H_2.\) The relation between the horizontal range of the projectile \(R\) and \(H_1\) and \(H_2\) is: 

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 the above