A ball drops from a ceiling of a room and after rebounding twice from the floor reaches a height equal to half that of the ceiling. Show that the coefficient of restitution is `sqrt(1/2)`
Text Solution
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Let `h=`height of ceiling `implies` speed before the first impact `=sqrt(2gh)` `implies` speed after the first impact `=esqrt(2gh)` the ball comes back for the second impact. Before the second impact, speed `=esqrt(2gh)` after the second impact, speed `=e^(2)sqrt(2gh)` Height attained `=u^(2)/(2g)impliesh/2=([e^(2)sqrt(2gh)]^(2))/(2g)impliesh/2=(e^(4)(2gh))/(2g)` `=e=1/root(4)(2)`
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