$A$ 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 $g = 10\ m/s^2$)

In the first second of its flight,a rocket ejects $1/60$ of its mass with a velocity of $2400\,m/s$. The acceleration of the rocket is ............ $m/s^2$.

The motion of a rocket in an upward direction with high speed is based on the principle of conservation of:

$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate $\frac{dM}{dt} = \alpha v$,where $M$ is the mass,$v$ is the velocity of the satellite,and $\alpha$ is a constant. What is the deceleration of the satellite?

$A$ flexible chain of length $L = 2 \ m$ and mass $M = 1 \ kg$ is initially held in a vertical position such that its lower end just touches a horizontal surface. It is released from rest at time $t = 0$. Assuming that any part of the chain that strikes the plane immediately comes to rest and that the portion of the chain lying on the horizontal surface does not form any heap,find the height of its centre of mass above the surface at the instant $t = 1/\sqrt{5} \ s$ (before it completely comes to rest).

$A$ train is moving with a velocity of $20 \, m/s$. Dust is falling on it at the rate of $50 \, kg/min$. The extra force required to move this train with a constant velocity will be ....... $N$.