Hello,

The velocity of ball is u m/s

The velocity of descending balloon is v m/s

Therefore, the velocity of ball w.r.t. balloon is u + v m/s

Now, the ball will pass the balloon when the relative displacement between the two is zero.

Now, displacement is given by, s = u't + 1/2 * a * t^2

= s = (u + v)*t - 1/2 * g * t^2 = 0 [ a = (-g) = acceleration due to gravity and u' = u + v]

Taking t common, we have:

t * [ (u + v) - 1/2 * g * t ] = 0 which gives t = 0 or [ (u + v) - 1/2 * g * t ] = 0

Since t cannot be equal to 0, therefore, we have: [ (u + v) - 1/2 * g * t ] = 0

Rearranging and solving the above equation, we get:

t = 2 * ( u + v ) / g (Answer)