Let the absolute velocities of the balloon be 'v1' and ball be 'v2'.

• Given$v_1=5$ and$v_2 - v_1 = 2$
• Hence$v_2 - 5 = 2$
• $v_2 = 7$
• After 't' secs let the ball return to the balloon. Its velocity decreases as the ball moves under gravity, finally ball reaches to the balloon during its upward journey.
• Displacement of balloon after 't' secs = 5t
• For ball,$u = 7$ and$a = -g = - 9.81 m/s ^2$.

$s = u t + \frac 1 2 at^2$

$s = 7 t + \frac 1 2 (-9.81)t^2$

$s = 7 t - \frac 1 2 \times 9.81 \times t^2$

$s = 7t - 4.905 \times t^2$........... equation (1)

• For ball and balloon to meet each other; Displacement of balloon = Displacement of ball
• Substituting$s = 5t$ in equation (1)
• Hence$5t = 7t - 4.905 \times t^2$

$4.905 t^2 - 2t = 0$

$t(4.905 t - 2) = 0$

• $Hence \:t = 0 \,s\: or \:t = 0.4077 \,s$
• The ball will return to the balloon after a total time interval = 0.4077 s.