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. \(4~\text{km/hr}\)

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.

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?

At the highest point of trajectory in the ground to the ground projectile, the angle between gravitational acceleration and momentum is

(1) 30°

(2) 45°

(3) 90°

(4) Data insufficient

A man wants to cross a river 600 m wide flowing at 8 m/s in the shortest time. Man has a speed of 6 m/ s in still water. What is the path length covered by the man in the river?

1. Infinite

2. 1 km

3. 100 m

4. 1000 cm

A shell is fired vertically upward with a velocity of \(20\) m/s from a trolley moving horizontally with a velocity of \(10\) m/s. A person on the ground observes the motion of the shell-like a parabola whose horizontal range is: (\(g= 10~\text{m/s}^2\)${\mathrm{}}^{}$)

A particle is moving along a circular path of radius a with constant angular velocity $\mathrm{\omega }$. The magnitude of displacement of the particle as a function of time t is:

1.  $\mathrm{a}<mspace\; width="1em"></mspace>\cos <mspace\; width="1em"></mspace>\mathrm{\omega t}$

2.  $\mathrm{a}<mspace\; width="1em"></mspace>\cos <mspace\; width="1em"></mspace>\frac{\mathrm{\omega t}}{2}$

3.  $\mathrm{a}<mspace\; width="1em"></mspace>\sin <mspace\; width="1em"></mspace>{\mathrm{\omega t}}^2$

4.  $2\mathrm{a}<mspace\; width="1em"></mspace>\sin <mspace\; width="1em"></mspace>\frac{\mathrm{\omega t}}{2}$

In the given diagram shown for a projectile, what is the angle of projection?

1.  ${\tan }^{-1}\left(4\right)$

2.  ${\tan }^{-1}\left(\frac{8}{3}\right)$

3.  ${\tan }^{-1}\left(\frac{4}{3}\right)$

4.  ${\tan }^{-1}\left(\frac{5}{3}\right)$

A body is executing uniform circular motion in a circle of radius 100 m at speed 10 m/s. Acceleration of the body is :

(1) Zero

(2) 2 $\mathrm{m}/{\mathrm{s}}^2$

(3) 1 $\mathrm{m}/{\mathrm{s}}^2$

(4) 5 $\mathrm{m}/{\mathrm{s}}^2$

An object of mass m is projected from the ground with a momentum \(p\) at such an angle that its maximum height is \(\frac{1}{4}\)th of its horizontal range. Its minimum kinetic energy in its path will be: