A ball is dropped from a balloon ascending at a speed of 7 m/s . If the balloon was at a height of 60 m at the time the ball was dropped, determine the time taken by the ball to reach the ground in seconds.

Step-by-step solution

Taking the upward direction as positive. Initial velocity of the ball, u = 7 m/s Displacement of the ball, s = -60 m Acceleration due to gravity, a = -9.8 m/s ^2 Using the equation of motion s = ut + 1 2 at^2 : -60 = 7t - 1 2 (9.8)t^2 -60 = 7t - 4.9t^2 4.9t^2 - 7t - 60 = 0 Multiplying by 10 on both sides: 49t^2 - 70t - 600 = 0 49t^2 - 210t + 140t - 600 = 0 7t(7t - 30) + 20(7t - 30) = 0 (7t + 20)(7t - 30) = 0 Since time cannot be negative, we get 7t - 30 = 0 t = 30 7 s .