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 ............ $m/s^2$.

$A$ rocket is ejecting $50\,g$ of gases per second at a speed of $500\,m/s.$ The accelerating force on the rocket will be ............ $N$.

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 $, W$)

An isolated rail car originally moving with speed $v_0$ on a straight,frictionless,level track contains a large amount of sand. $A$ release valve on the bottom of the car malfunctions,and sand begins to pour out straight down relative to the rail car. What happens to the speed of the rail car as the sand pours out?

$A$ $600\; kg$ rocket is set for a vertical firing. If the exhaust speed is $1000\; m/s$,the mass of the gas ejected per second (in $kg/s$) to supply the thrust needed to overcome the weight of the rocket is

$A$ $5000\, kg$ rocket is set for vertical firing. The exhaust speed is $800\, m/s$. To give an initial upward acceleration of $20\, m/s^2$,the amount of gas ejected per second to supply the needed thrust will be ........... $kg/s$ $(g = 10\, m/s^2)$. (in $.5$)