$A$ rocket is fired vertically from the ground with a resultant vertical acceleration of $10 \,m/s^2$. The fuel is exhausted in $1 \,min$ and it continues to move up. What is the maximum height reached (in $\,km$)?

$A$ rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \,m/s^2$. If after $5 \,s$ its engine is switched off,the maximum height of the rocket from the earth's surface would be.........$m$

If the force on a rocket having an exhaust velocity of $300 \, m/s$ is $210 \, N$,then the rate of combustion of the fuel is ........... $kg/s$.

$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t} = \alpha v$,where $M$ is the mass,$v$ is the speed of the satellite,and $\alpha$ is a constant. The acceleration of the satellite is:

$A$ rocket is fired vertically up from the ground with a resultant vertical acceleration of $10\ m/s^2$. The fuel is finished in $1\ minute$ and it continues to move up. $(a)$ Find the maximum height reached. $(b)$ After how much time from then will the maximum height be reached? (Take $g = 10\ m/s^2$)

$A$ flat plate moves normally with a speed $v_1$ towards a horizontal jet of water of uniform area of cross-section. The jet discharges water at the rate of volume $V$ per second at a speed of $v_2$. The density of water is $\rho$. Assume that water splashes along the surface of the plate at right angles to the original motion. The magnitude of the force acting on the plate due to the jet of water is