$A$ ball is hit by a batsman at an angle of $37^o$ with an initial velocity $u = 15 \ m/s$ as shown in the figure. The man standing at $P$ is at a distance of $9 \ m$ from the point $B$ where the ball would strike the ground. What is the minimum velocity at which the man should run to catch the ball before it hits the ground? Assume the height of the man is negligible. ........ $m/s$

$A$ car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud,as they leave the ground,are thrown:

$A$ hill is $500 \, m$ high. Supplies are to be sent across the hill,using a cannon that can hurl packets at a speed of $125 \, m/s$ over the hill. The cannon is located at a distance of $800 \, m$ from the foot of the hill and can be moved on the ground at a speed of $2 \, m/s$; so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach the ground on the other side of the hill? Take $g = 10 \, m/s^2$.

The initial position of an object at rest is given by $3 \hat{i}-8 \hat{j}$. It moves with constant acceleration and reaches the position $2 \hat{i}+4 \hat{j}$ after $4 \, s$. What is its acceleration?

$A$ particle is moving eastwards with a velocity of $5\,m/s$. In $10\,s$,the velocity changes to $5\,m/s$ northwards. The average acceleration in this time is

$A$ projectile of mass $200 \ g$ is launched in a viscous medium at an angle $60^{\circ}$ with the horizontal,with an initial velocity of $270 \ m/s$. It experiences a viscous drag force $\vec{F} = -c \vec{v}$,where the drag coefficient $c = 0.1 \ kg/s$ and $\vec{v}$ is the instantaneous velocity of the projectile. The projectile hits a vertical wall after $2 \ s$. Taking $e = 2.7$,the horizontal distance of the wall from the point of projection (in $m$) is