Sand is falling on a flat car being pulled with constant speed. The rate of mass falling on the cart is constant. Then the horizontal component of force exerted by the falling sand on the cart,

A mass ${\mathrm{m}}_1$is connected by a weightless cable passing over a frictionless pulley to a container of water, whose mass is ${\mathrm{m}}_0$ at $t=0.$ If the container ejects water in downward direction at a constant rate $b \mathrm{kg} s^{-1}.$ With a velocity $v_0$ relative to the container, determine the acceleration of ${\mathrm{m}}_1$ as a function of time.

A uniform chain of mass $\mathrm{m} = 1\mathrm{kg}$ and length $l = 1\mathrm{m}$ hangs on a thread and touches the surface of a table by its lower end. Find the force exerted by the table on the chain when $\mathrm{x} = 0.5 \mathrm{m}$ length of chain has fallen on the table. The fallen part does not form heap.

A smooth container filled with water moves with a velocity $v_0.$ If water leaks at the base with a constant rate $\mu \mathrm{kg}/\mathrm{s},$ find the velocity and acceleration of the container as the function of time. Assume $M=$ initial mass of the system (container $+$ water).

A rocket has initial velocity $v_0$ and mass ${\mathrm{m}}_0.$ If it travels in free space, find the velocity of the rocket as the function of its existing mass $M.$ Assume that that rocket expels the fuel with a velocity $u_{rel}$ with respect to itself.

A cart is pulled with a constant force $F$ with a constant velocity $v$ on a smooth horizontal ground. A Hooper loads the cart with sands at a time of $\mu \mathrm{kg}/\mathrm{s}.$ Find the:

(i) External force $F$
(ii) The power delivered by the external force.
(iii) The rate of change of kinetic energy.

A block of mass $M$ is kept on a smooth horizontal surface. A jet of water emerging from a nozzle of cross-section, it strikes the block horizontally with a speed $u.$ Assuming $\rho$ as the density of water.

(i) Find the maximum power applied on the block.
(ii) Calculate the thrust imparted by water jet on the block at this time.
(ii) Obtain an expression for the speed of the block as the function of time.