A basketball is dropped from a hieght of 2.00 metersabove the ground. On the fir

Question

A basketball is dropped from a hieght of 2.00 metersabove the ground. On the first bounce the ball reaches amaximum height of 1.10 meters where it is caught. Find the velocityof the ball: a. just before it makes contact with the ground? b.just after it leaves the ground after thebounce? Also find the total time from drop to catch (neglecting thetime the ball is in contact with the ground) c. How much energy is lost during the bounce? Assume the ballwieghs 0.2 kg A basketball is dropped from a hieght of 2.00 metersabove the ground. On the first bounce the ball reaches amaximum height of 1.10 meters where it is caught. Find the velocityof the ball: a. just before it makes contact with the ground? b.just after it leaves the ground after thebounce? Also find the total time from drop to catch (neglecting thetime the ball is in contact with the ground) c. How much energy is lost during the bounce? Assume the ballwieghs 0.2 kg

Explanation / Answer

initial height h = 2 m final height h ' = 1.1 m (a). velocity of the ball just before it makes contact withthe ground v = [ 2gh ]           v =6.26 m / s (b). velocity of the ball just after leaves the ground v' = [ 2gh ' ]                                                                                    =4.64 m / s (c). Time T = t + t '                   = [ 2h / g ] + [ 2h ' / g ]                   = 0.6388 + 0.473                   = 1.112 s (d). Energy lost = ( 1/ 2) m v ^ 2 - ( 1/ 2) m v' ^2                         = 0.5 * m * [ 6.26 ^ 2 - 4.64 ^ 2 ]                         = 1.7658 J

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