Motion in A Str...

A man can swim with a speed of 4 $$km h^{-1}$$ in still water. He crosses a river 1 km wide that flows steadily at 3 $$kmh^{-1}$$. If he makes his strokes normal to the river current, how far down the river does he go when he reaches the other bank?

A rocket of initial mass $$6000\ kg$$ eject gases at a constant rate of $$16\ kg s^{-1}$$ with constant relative speed of $$11\ kms^{-1}$$. What is the acceleration of rocket one minute after the blast?

A car travels with a uniform velocity of $$20\,\,m{s^{ - 1}}$$ for 5 sec. The brakes are then applied and the car is uniformly retarded. It comes to rest in further 8 sec  by drawing a graph between velocity and time-find.

A ball rolls off the top of a stairway horizontally with a velocity of $${ 4.5\ ms }^{ -1 }$$. Each steps is $$0.2\ m$$ high and $$0.3\ m$$ wide. If $$g$$ is $${ 10\ ms }^{ -2 }$$, and the ball strikes the edge of the $$nth$$ step, then $$n$$ is equal to:

A body is dropped from a balloon moving up with a velocity of $$4\ m/s$$ when the balloon is at a height of $$120.5\ m$$ from the ground. The height of the body after $$5\ s$$ from the ground is? $$(g = 9.8\ ms^{-2})$$.

The displacement of a body at any time $$t$$ after starting is given by $$s = 15t - 0.4 t^{2}$$. Find the time when the velocity of the body will be $$7\ ms^{-1}$$.

A balloon is ascending vertically with an acceleration of 1 $$ms^{-2}$$. Two stones are dropped from it at an interval of 2 s. Find the distance between them 1.5 s after the second stone is released.

A car starting from rest accelerates at the rate $$f$$ through a distance $$S$$, then continues at constant speed for time $$t$$ and then decelerates at the rate $$f/2$$ to come to rest. If the total distance traversed is $$5\ S$$, then

A ball of mass $$0.2kg$$ is thrown vertically upwards by applying a force by hand. If the hand moves $$0.2m$$ which applying the force and the ball goes upto $$2m$$ height further, find the magnitude of the force. Consider $$g=10m/{s}^{2}$$

A parachutist after bailing out falls $$50\ m$$ without friction. When parachute opens, it decelerates at $$2\ m/s^{2}$$. He reaches the ground with a speed of $$3\ m/s$$. At what height, did he bail out?