$A$ rocket of initial mass $1500 \ kg$ ejects gas at a constant rate of $10 \ kg/s$ with a relative speed of $5 \ km/s$. What is the acceleration of the rocket $50 \ s$ after the launch,neglecting gravity (in $m/s^2$)?

The initial mass of a rocket is $1000 \, \text{kg}$. Calculate at what rate the fuel (in $\text{kg s}^{-1}$) should be burnt so that the rocket is given an acceleration of $20 \, \text{m s}^{-2}$. The gases come out at a relative speed of $500 \, \text{m s}^{-1}$ with respect to the rocket. [Use $g = 10 \, \text{m s}^{-2}$]

Can the flight of a rocket be considered projectile motion? Give reasons.

Sand is being dropped from a stationary dropper at a rate of $0.5 \, kg s^{-1}$ on a conveyor belt moving with a velocity of $5 \, m s^{-1}$. The power needed to keep the belt moving with the same velocity will be: (in $, W$)

$A$ rocket works on the principle of conservation of which of the following?

Sand is being dropped on a conveyor belt at the rate of $M \ kg/s$. The force necessary to keep the belt moving with a constant velocity of $v \ m/s$ will be