A ship $A$ is moving westward with a speed of $10~\text{kmph}$ and a ship $B,$ $100 ~\text{km}$ south of $A,$ is moving northward with a speed of $10~\text{kmph}.$ The time after which the distance between them becomes the shortest is:
1. $0~\text{h}$ 
2. $5~\text{h}$ 
3. $5\sqrt{2}~\text{h}$ 
4. $10\sqrt{2}~\text{h}$ 

Two particles ${A}$ and ${B}$, move with constant velocities $\vec{v}_1$ and $\vec{v}_2$ respectively. At the initial moment, their position vectors are $\vec{r}_1$ and $\vec r_2$ respectively. The conditions for particles ${A}$ and ${B}$ for their collision will be:

A projectile is fired from the surface of the earth with a velocity of $5~\text{m/s}$ and at an angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3~\text{m/s}$ at the same angle follows a trajectory that is identical to the trajectory of the projectile fired from the Earth. The value of the acceleration due to gravity on the other planet is: (given $g=9.8~\text{m/s}^2$ )
1. $3.5~\text{m/s}^2$
2. $5.9~\text{m/s}^2$
3. $16.3~\text{m/s}^2$
4. $110.8~\text{m/s}^2$

The velocity of a projectile at the initial point $A$ is $2\hat i+3\hat j~\text{m/s}.$ Its velocity (in m/s) at the point $B$ is:
              

A particle moves in a circle of radius $5$ cm with constant speed and time period $0.2\pi$ s. The acceleration of the particle is:

A body is moving with a velocity of $30~\text{m/s}$ towards the east. After $10~\text s,$ its velocity becomes $40~\text{m/s}$ towards the north. The average acceleration of the body is:
1. $7~\text{m/s}^2$
2. $\sqrt{7}~\text{m/s}^2$
3. $5~\text{m/s}^2$
4. $1~\text{m/s}^2$

A missile is fired for a maximum range with an initial velocity of $20~\text {m/s}.$ If $g=10~\text{m/s}^2,$ then the range of the missile will be:

A projectile is fired at an angle of $45^\circ$ with the horizontal. The elevation angle $\alpha$ of the projectile at its highest point, as seen from the point of projection is:
1. $60^\circ$
2. $tan^{-1}\left ( \frac{1}{2} \right )$
3. $tan^{-1}\left ( \frac{\sqrt{3}}{2} \right )$
4. $45^\circ$