A rocket accelerates straight up by ejecting gas downwards. In a small time, interval $△ t,$ it ejects a gas of mass $△ m$ at a relative speed $u .$ Calculate $K E$ of the entire system at $t$ $+$ $△ t$ and $t$ and show that the device that ejects gas does work $\frac{1}{2} △ m u^{2}$ in this time interval (neglect gravity).

Question

A rocket accelerates straight up by ejecting gas downwards. In a small time, interval

△ t,

it ejects a gas of mass

△ m

at a relative speed

u .

Calculate

K E

of the entire system at

t

+

△ t

and

t

and show that the device that ejects gas does work

\frac{1}{2} △ m u^{2}

in this time interval (neglect gravity).

Toppr Admin · Accepted Answer