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Question Number 16634 by Tinkutara last updated on 24/Jun/17

Consider a rubber ball freely falling  from a height h = 4.9 m onto a  horizontal elastic plate. Assume that  the duration of collision is negligible  and the collision with the plate is  totally elastic. Then the velocity as a  function of time and the height as  function of time will be

$$\mathrm{Consider}\:\mathrm{a}\:\mathrm{rubber}\:\mathrm{ball}\:\mathrm{freely}\:\mathrm{falling} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{height}\:{h}\:=\:\mathrm{4}.\mathrm{9}\:\mathrm{m}\:\mathrm{onto}\:\mathrm{a} \\ $$$$\mathrm{horizontal}\:\mathrm{elastic}\:\mathrm{plate}.\:\mathrm{Assume}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{duration}\:\mathrm{of}\:\mathrm{collision}\:\mathrm{is}\:\mathrm{negligible} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{collision}\:\mathrm{with}\:\mathrm{the}\:\mathrm{plate}\:\mathrm{is} \\ $$$$\mathrm{totally}\:\mathrm{elastic}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{as}\:\mathrm{a} \\ $$$$\mathrm{function}\:\mathrm{of}\:\mathrm{time}\:\mathrm{and}\:\mathrm{the}\:\mathrm{height}\:\mathrm{as} \\ $$$$\mathrm{function}\:\mathrm{of}\:\mathrm{time}\:\mathrm{will}\:\mathrm{be} \\ $$

Commented by Tinkutara last updated on 24/Jun/17

Commented by Tinkutara last updated on 24/Jun/17

Answered by ajfour last updated on 24/Jun/17

initial velocity is zero, it gradually  decreases, then hits the plate when  at maximum negative velocity  which becomes as much +ve in  zero time, then decreases gradually  to its max. negative value where  upon it hits the plate again.   such behaviour is depicted for   v-t  and  y-t only in option (3) .

$$\mathrm{initial}\:\mathrm{velocity}\:\mathrm{is}\:\mathrm{zero},\:\mathrm{it}\:\mathrm{gradually} \\ $$$$\mathrm{decreases},\:\mathrm{then}\:\mathrm{hits}\:\mathrm{the}\:\mathrm{plate}\:\mathrm{when} \\ $$$$\mathrm{at}\:\mathrm{maximum}\:\mathrm{negative}\:\mathrm{velocity} \\ $$$$\mathrm{which}\:\mathrm{becomes}\:\mathrm{as}\:\mathrm{much}\:+\mathrm{ve}\:\mathrm{in} \\ $$$$\mathrm{zero}\:\mathrm{time},\:\mathrm{then}\:\mathrm{decreases}\:\mathrm{gradually} \\ $$$$\mathrm{to}\:\mathrm{its}\:\mathrm{max}.\:\mathrm{negative}\:\mathrm{value}\:\mathrm{where} \\ $$$$\mathrm{upon}\:\mathrm{it}\:\mathrm{hits}\:\mathrm{the}\:\mathrm{plate}\:\mathrm{again}. \\ $$$$\:\mathrm{such}\:\mathrm{behaviour}\:\mathrm{is}\:\mathrm{depicted}\:\mathrm{for} \\ $$$$\:\mathrm{v}-\mathrm{t}\:\:\mathrm{and}\:\:\mathrm{y}-\mathrm{t}\:\mathrm{only}\:\mathrm{in}\:\mathrm{option}\:\left(\mathrm{3}\right)\:. \\ $$

Commented by Tinkutara last updated on 24/Jun/17

Thanks Sir!

$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$

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