If energy cannot be created or destroyed, why doesn't the ball bounce back up to the same height it was dropped at?

Acave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. the lift is performed in three stages, each requiring a vertical distance of 10.0 m: (a) the initially stationary spelunker is accelerated to a speed of 4.90 m/s; (b) he is then lifted at the constant speed of 4.90 m/s; (c) finally he is decelerated to zero speed. how much work is done on the 68.0 kg rescue by the force lifting him during each stage?

Karen is running forward at a speed of 9 m/s. she tosses her sweaty headband backward at a speed of 20 m/s. the speed of the headband, to the nearest whole number relative to a stationary observer watching karen

Air is to be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. air enters the heat exchanger at 95 kpa and 20°c at a rate of 0.6 m^3/s. the combustion gases (cp = 1.10 kj/kg°c) enter at 160°c at a rate of 0.95 kg/s and leave at 95°c. determine the rate of heat transfer to the air and its outlet temperature.