A missile is fired for maximum range with an initial velocity of \(20\) m/s, then the maximum height of missile is: (Take \(g=10\) m/s²)
1. \(20\) m
2. \(30\) m
3. \(10\) m
4. \(40\) m

A particle is moving along a circle of radius \(R \) with constant speed \(v_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?

An open trolley is moving on a horizontal road with constant velocity \(v_1\). A man on the trolley throws a ball vertically upward (with respect to trolley) with velocity \(v_2\). Select the correct statement.

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 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