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?

A bullet fired into a fixed target loses half of its velocity after penetrating $$3$$ $$cm.$$ How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

A smooth block is released at rest on a $${45^ \circ }$$ incline and then slides a distance $$'d'$$. The time taken to slide is $$'n'$$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A particle of mass 0.3 kg subjected to a force $$F=-kx$$ with $$k=15$$ $$N/m$$. What will be its initial acceleration if it is released from a point 20 cm away from the origin?