It is raining at \(20\) m/s in still air. Now a wind starts blowing with speed \(10\) m/s in the north direction. If a cyclist starts moving at \(10\) m/s in the south direction, then the apparent velocity of rain with respect to a cyclist will be:
1. \(20\) m/s
2. \(20\sqrt{2}\) m/s
3. \(10 \sqrt{5}\) m/s
4. \(30\) m/s

A body of mass 2 kg is projected at a speed of 20 m/s from a pillar of height 40 m at an angle of 30° with the horizontal in an upward direction. The speed with which it will hit the ground is

(1) 30 m/s

(2) 20$\sqrt{3}$ m/s

(3) 25 m/s

(4) 40 m/s

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 \(v_0\). 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.  $\sqrt{\frac{2{\mathrm{u}}_1{\mathrm{u}}_2}{\mathrm{g}}}$