A man is walking on a horizontal road at a speed of \(4~\text{km/hr}.\) Suddenly, the rain starts vertically downwards with a speed of \(7~\text{km/hr}.\) The magnitude of the relative velocity of the rain with respect to the man is:
1. \(\sqrt{33}~\text{km/hr}\)
2. \(\sqrt{65}~\text{km/hr}\)
3. \(8~\text{km/hr}\)
4. \(4~\text{km/hr}\)

A particle of mass 6 kg moves with an initial velocity of $\overrightarrow{\mathrm{v}} = \left(8\hat{\mathrm{i}} + 8\hat{\mathrm{j}}\right)$ m/s. A constant force of $\overrightarrow{\mathrm{F}}=-30\hat{\mathrm{j}}$ N is applied to the particle. Initially, the particle was at (0, 0). The x-coordinate of the particle, when its y-coordinate again becomes zero is given by

(1) 6.0 m 

(2) 12.8 m

(3) 8 m

(4) 25.6 m

In a uniform circular motion:

(1) Velocity and acceleration remain constant.

(2) Kinetic energy remains constant.

(3) Speed and acceleration changes.

(4) Only velocity changes, acceleration remains constant.

If a body is accelerating, then:

Compared to an ideal projectile motion under gravity, which of the following is incorrect regarding another projectile motion in which air friction is also considered?

Two balls are projected to acquire same range with the same initial speed u but at different angles of projection. If maximum height acquired by balls are ${\mathrm{H}}_1 \mathrm{and} {\mathrm{H}}_2$, then (${\mathrm{H}}_1 + {\mathrm{H}}_2$) is: (angle of projection of one projectile is $\mathrm{\theta }$)

(1) ${\tan }^2 \theta$

(2) ${\cot }^2 \mathrm{\theta }$

(3) $\frac{{\mathrm{u}}^2}{2\mathrm{g}}$

(4) tan $\mathrm{\theta }$

At the highest point of trajectory in the ground to the ground projectile, the angle between gravitational acceleration and momentum is

(1) 30°

(2) 45°

(3) 90°

(4) Data insufficient

A particle revolves in a horizontal circle with decreasing velocity. The angle between instantaneous velocity and instantaneous acceleration of the particle at an instant is

(1) < 90°

(2) > 90°

(3) = 90°

(4) $\ge$ 90°

Two projectiles are thrown horizontally from a high cliff in the opposite direction with the same speed 20 m/ s simultaneously. At what time velocities of both particles become perpendicular?

(1) 2$\sqrt{2}$ s

(2) 2 s

(3) 4 s

(4) 4$\sqrt{2}$ s