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CBSE Class 12-science Answered

when the ball is released from height 5m it rebounds to the height of 3m. with whate velocity it should be dropped so that it rebounds its height 
Asked by sbtech357 | 23 Jul, 2018, 10:28: AM
answered-by-expert Expert Answer
when the ball dropped from 5m height, the ball hit the ground with velocity vi ,
which is given by begin mathsize 12px style v subscript i space equals space square root of 2 cross times g cross times h end root space equals space square root of 2 cross times 9.8 cross times 5 end root space space equals space 9.9 space m divided by s end style ...................(1)
when the ball rebound to a height 3 m, then the rebound velocity vo at ground is given by, begin mathsize 12px style v subscript o equals space square root of 2 cross times g cross times h end root space equals space square root of 2 cross times 9.8 cross times 3 end root space equals 7.7 space m divided by s end style
velocity reduction ratio = 7.7/9.9 = 7/9
 
from (1), we know if the ball rebounds with same velocity 9.9 m/s it will reach the height 5 m.
if we consider the velocity reduction ratio, then the ball should hit the ground with velocity 9.9×(9/7) = 12.73 m/s
 
to get the velocity 12.73 m/s at ground, the ball should be given some initial veleocity instead of just dropping the ball. 
 
This initial velocity u is calculated from relation " v2  = u2 + 2gh ", where u is initial velocity and v is final velocity, h is height
 
then we get begin mathsize 12px style u space equals space square root of v squared minus 2 cross times g cross times h end root space equals space square root of 12.73 squared minus 2 cross times 9.8 cross times 5 end root space end style = 8 m/s

Answered by Thiyagarajan K | 23 Jul, 2018, 11:15: AM

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