A ball is thrown vertically upwards. It was observed at a height h twice after a time interval `Deltat`. The initial velocity of the ball is

Options

A. ` sqt ( 8 gh +g^(2) (Delta t)^(2)) `
B. ` sqrt( 8h +4g^(2) (Delta t)^(2))`
C. ` (1)/(2) sqrt( 8gh +g^(2) ( Delta t)^(2))`
D. None of these

Answer

C

Explanation

Let u : initial velocity of the ball t: time to reach at height h ` rArr " " h=ut- g t ^(2)//2 rArr g t^(2) -2ut +2h =0 ………….Delta t = ` diff in roots
` t_1 +t_2 =(2u)/(g) ,t_1t_2 =(2h)/(g) " "," " (t_1-t_2)^(2) =(t_1+t_2) ^(2) -4t_1t_2`
` rArr " "(Delta t)^(2) =(4u^(2))/(g^(2)) -(8h)/(g) rArr =(sqrt(8gh +g^(2) Delta t^(2))/(2) `