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

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 $\mathrm{\theta }$