$A$ 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.........$m$

An ice block is melting at a constant rate $\left| \frac{dm}{dt} \right| = \mu$. Its initial mass is $m_0$ and it is moving with velocity $v$ on a frictionless horizontal surface. The distance travelled by it until it melts completely is:

$A$ heap of rope with mass density $\lambda$ (per unit length) lies on a table. You grab one end and pull horizontally with constant speed $v$,as shown in the figure. (Assume that the rope has no friction with itself in the heap.) The force that you must apply to maintain the constant speed $v$ is

$A$ rocket of mass $5700 \,kg$ ejects mass at a constant rate of $15 \,kg/s$ with a constant speed of $12 \,km/s$. The acceleration of the rocket $1 \,minute$ after the blast is ........... $m/s^2$ $(g=10 \,m/s^2)$.

$A$ rocket motor consumes $100 \ kg$ of fuel per second,exhausting it with a speed of $5 \ km/s$. The speed of the rocket when its mass is reduced to $\frac{1}{20}$ of its initial mass is (Assume initial speed to be zero and ignore gravitational and viscous forces.)

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