Kinematics (Free fall)
Two balls are projected ( one vertically upwards and the other vertically downwards) with initial velocity from a height . They take 8 seconds and 2 seconds respectively to reach the ground.
Another ball is dropped from the same height and it takes seconds for it to reach the ground. Find the value of .
The answer is 4.
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Considering downward direction as positive and upward direction as negative, we get 3 equations of motion, which are..
h= -uT(1)+0.5gT(1)^2 .......... (A)
h= uT(2)+0.5gT(2)^2............(B)
h= 0.5gT^2...............(C)
Where T(1) is the time taken when ball is thrown upwards, T(2) is the time taken when the ball is thrown downwards and T is the time taken when the ball is just released.
Eliminating h from equations( A) and (B), we have u=0.5g[T(2)+T(1)]
Eliminating h from equations (C) and (A), we have uT(1)=0.5g[T(1)^2-T^2]
Comparing values of (u) from above equations.. We get T=[T(1)*T(2)]^(0.5)