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?

1.	The time of flight decreases.
2.	Decrease in the horizontal component of velocity continuously.
3.	The angle with horizontal is less at the time of striking the ground compared to the angle of projection with horizontal.
4.	The angle with the vertical is less at the time of striking the ground with respect to the angle of projection with vertical.

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:

Which of the following is the angle between velocity and acceleration of a body in uniform circular motion?
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(90^\circ\)

A person is rotating in a horizontal circle of radius 7 m. Find the period of rotation for which the acceleration is equal to 3g.

(1) 2.6 s

(2) 2.8 s

(3) 3.1 s

(4) 4.3 s