A balloon rising vertically up with unitrom velcity ` 15 ms^(-1)` releases a ball at a deight of ` 100 m`. Calculate the time taken by the ball to hit the ground and total height of balloon when ball hits the ground. Take ` g= 10 md^(-2)`.

Explanation

Taking vertical downward motin of ball released from the balloon rising vertically upward, upto ground, we have ltbRgt ` u=-0 15 ms^(-1) , a = g = 10 ms^(-2)` , S = 100 m`,
` t= ?`
` S= ut + 1/2 at^2`
` 100 =- 15 xx t + 1/2 xx 10 xx t^2 =- 15 + 5 t^2`
or ` t^2 - 3 t- 20 = 0`
` or r^2 - 3 t- 20 =0`
or 1 t= ( 3 +- sqrt ( 9+ 80)/2 = (3 =- 9.4)/2 = 6. 2 s or ` -3.2 s`
As time cannot be negative, so ` t= 6.2 s`
Taking further upward motion of balloon from height ` 100o m` the heith attained by balloon in ` 6.2 s= 15 xx 6.2 = 93 .0` m
Total height of balloon ` = 100 + 93.0`
` = 193 m` .