3.12 A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one-tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.

 

Taking vertical downward motion of ball from a height 90 m, we have
u=0,a=10m/s2,h=90m
t=2ha=2×9010=32s=4.24s
v=2as=2×10×90=302m/s
Reboundvelocityofball,
u'=910v=910×302=272m/s
Timetoreachhighestpoint,t'=u'a=27210=3.81s
Totaltime=t+t'=4.24+3.81=8.05s
Theballwilltakefurther3.81stofallbacktofloor.
Velocitybeforestrikingthefloor=272m/s
Velocityofballafterstrikingthefloor
=910×272=24.32m/s
Totaltimeelapsedbeforeupwardmotionofball=8.05+3.81=11.86s
The speed-time graph of the ball is represented in the given figure as: