A trolley containing water has total mass $4000\, kg$ and is moving at a speed of $40\, m/s$. Now water start coming out of a hole at the bottom of the trolley at the rate of $8\,kg/s$. Speed of trolley after $50\, s$ is ............ $m/s$

A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of $12 \;m/ s$.

If the mass of the ball is $0.15 \;kg$, determine the impulse (in $N\;s$) imparted to the ball. (Assume linear motion of the ball)

The position-time graph of a body of mass $2\, kg$ is as given in figure. What is the impulse on the body at $t = 0\, s$ and $t = 4\, s$.

The time in which a force of $2 \,N$ produces a change of momentum of $0.4\,kg - m{s^{ - 1}}$ in the body is ......... $\sec$

An object of mass $m$ is projected 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

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m =0.4 kg$ is at rest on this surface. An impulse of $1.0 N s$ is applied to the block at time $t =0$ so that it starts moving along the $x$-axis with a velocity $v ( t )= v _0^{ e ^{-1 / \tau}}$, where $v_0$ is a constant and $\tau=4 s$. The displacement of the block, in metres, at $t=\tau$ is. . . . . . . Take $e ^{-1}=0.37$