A rocket fired vertically upwards with constant acceleration has its fuel exhausted in $10 \mathrm{s}$. What is the maximum height reached by the rocket if its velocity at the end of ${10}^{th}$ second is $600 \mathrm{m}/\mathrm{s}$

Assume $g=10 \mathrm{m}/{\mathrm{s}}^2$.

The velocity of a particle moving along a straight line is given by : $v=10+3t^2$. The change in velocity in the interval from $\mathrm{t}=2 \mathrm{s}$ and $\mathrm{t}=5 \mathrm{s}$ is

Two bodies are moving in two mutually perpendicular directions with speed $\vartheta$. The magnitude of their relative velocity is