$A$ balloon with mass $m$ is descending vertically with an acceleration $a$ (where $a < g$). The mass to be removed from the balloon so that it starts moving vertically up with an acceleration $a$ is:

$A$ soldier with a machine gun,falling from an airplane,gets detached from his parachute. He is able to resist the downward acceleration if he shoots $40$ bullets per second at a speed of $500 \,m/s$. If the mass of a bullet is $49 \,g$,what is the mass of the man with the gun in $kg$? Ignore air resistance and assume the acceleration due to gravity $g = 9.8 \,m/s^2$.

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

$A$ satellite moving with velocity $v$ in a force-free space collects stationary interplanetary dust at a rate of $\frac{dM}{dt} = \alpha v$,where $M$ is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is:

$A$ rocket which has a mass of $3.5 \times 10^4 \,kg$ is blasted upwards with an initial acceleration of $10 \,m/s^2$. The initial thrust of the blast is-

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