Path of a projectile with respect to another projectile so long as both remain in the air is:

1. Circular

2. Parabolic

3. Straight

4. Hyperbolic

A particle is thrown with velocity u making an angle $\mathrm{\theta }$ with the horizontal. It just crosses the top of two poles each of height h after 1 s and 3 s respectively. The time of flight of the particle is:

(1) 4 s

(2) 2 s

(3) 8 s

(4) 6 s

A projectile is moving in the XY plane such that the horizontal and vertical directions are along the X-axis and Y-axis respectively. The projectile is fired from the origin at a large height with initial velocity ($50\hat{\mathrm{i}} + 20\hat{\mathrm{j}}$) m/s. The time after which instantaneous velocity of the projectile becomes perpendicular to its initial velocity is:     (g=10m/s²)

(1) 7.5 s

(2) 14.5 s

(3) 5.5 s

(4) 10.5 s

A particle is thrown from the ground with a speed u at an angle $\mathrm{\theta }$ above the horizontal. The rate of change of velocity of the particle at the highest point of the path is:

1. gsin$\mathrm{\theta }$

2. gcos$\mathrm{\theta }$

3. g

4. Zero

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 \(\mathrm{v}_0\). 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 ${\mathrm{v}}_1$. 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