An aeroplane is flying vertically upwards. When it is at a height of $1000 \mathrm{m}$ above the ground and moving at a speed of $367 \mathrm{m} {\mathrm{s}}^{-1}$, a shot is fired at it with a speed of $567 \mathrm{m} {\mathrm{s}}^{-1}$ from a point directly below it. What should be the acceleration of the aeroplane so that it may escape from being hit?

A shot is fired at an angle $\mathrm{\theta }$ to the horizontal such that it strikes the hill while moving horizontally. Find the initial angle of the projection $\mathrm{\theta }$.

A man is riding on a horse. He is trying to jump the gap between two symmetrical ramps of snow separated by a distance $W$ as shown in the figure. He launches off the first ramp with a speed $V_{\mathrm{L}}$. The man and the horse have a total mass $m$ and their size is small as compared to $W$. The value of initial launch $V_{\mathrm{L}}$ speed which will put the horse exactly at the peak of the second ramp is

All the particles thrown with the same initial velocity would strike the ground