An open trolley is moving on a horizontal road with constant velocity ${\mathrm{v}}_1$. A man on the trolley throws a ball vertically upward (with respect to trolley) with velocity ${\mathrm{v}}_2$. Select the correct statement.

(1) Time of flight of the ball to a man on the ground and the man on the trolley will be different.

(2) Maximum height attained by the ball for both men will be different.

(3) Horizontal range of the ball for both men will be different.

(4) Horizontal range of the ball for both men will be the same.

Two stones are thrown simultaneously from the top of a building horizontally but in opposite directions, they will be moving perpendicular to each other say after time t, then t is equal to ___________. The initial speeds of stones are ${\mathrm{u}}_1 \mathrm{and} {\mathrm{u}}_2$ respectively and acceleration due to gravity is g.

1.  $\frac{{\mathrm{u}}_1{\mathrm{u}}_2}{\mathrm{g}}$

2.  $\sqrt{\frac{{\mathrm{u}}_1{\mathrm{u}}_2}{\mathrm{g}}}$

3.  $\sqrt{\frac{{\mathrm{u}}_1{\mathrm{u}}_2}{{\mathrm{g}}^2}}$

4.  $\sqrt{\frac{2{\mathrm{u}}_1{\mathrm{u}}_2}{\mathrm{g}}}$

Two projectiles projected with the same speed at angles $\mathrm{\theta }$ and (90° - $\mathrm{\theta }$) from the same point, then ${\mathrm{H}}_1 \times {\mathrm{H}}_2$ is equal to: (where symbols have their usual meanings)

1.  $\frac{{\mathrm{R}}^2}{16}$

2.  $\frac{{\mathrm{R}}^2}{8}$

3.  $\frac{{\mathrm{R}}^2}{4}$

4.  ${\mathrm{R}}^2$

A projectile is projected from the ground with speed 20 m/s at an angle 30° with vertical. The radius of curvature of the path of a projectile, when velocity makes 30° with horizontal is (g = 10 m/${\mathrm{s}}^2$)

(1) 8.5 m

(2) 15.4 m

(3) 26.2 m

(4) 32.6 m

A projectile is projected with speed u at an angle of 30° with the vertical from the ground. The angle between the acceleration of the projectile and its velocity at the time of striking the horizontal ground is:

(1) 30°

(2) 60°

(3) 45°

(4) 0°

Which of the following statements is incorrect?

A man is walking on a horizontal road with a speed of 4 km/h. Suddenly, the rain starts vertically downwards with a speed of 7 km/h. The magnitude of the relative velocity of the rain with respect to the man is:

1. $\sqrt{33}$ km/h

2. $\sqrt{65}$ km/h

3. 8 km/h

4. 4 km/h

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: