A man in a balloon, rising vertically with an acceleration of `5 m//s^(2)`, releases a ball 10 s after the balloon is let go from the ground. The greatest height above the ground reached by the ball is

Options

A. `14.7 m`
B. `19.6 m`
C. ` 9.8 m`
D. ` 24.5m `

Answer

A

Explanation

Height travelled by ball ( with ballon )in sec ,
` h_1=(1)/(2) a t^(2) =(1)/(2) xx 4.9 xx 2^(2) =9.8 m `
Velocity of the balloon after 2 sec
` v=a t= 4.9 xx 2 = 9.8 m//s `
Now if the ball is released from the balloon then it acquire same velocity in upward direction
Let it move up to maximum height `h_2`
` v^(2) =u^(2) -2gh_2 rArr 0= (9.8)^(2) -2xx ( 9.8) xxh_2 =4.9 m`
Greatest height above the ground reached by the ball ` =h_1 +h_2 =9.8 + 4.9 =14.7 m`