A ball thrown vertically upwards from the top of a tower of height 135 m takes 6 s longer to hit the ground than a ball thrown vertically downwards from the same position with the same speed. The initial speed of the balls is _____ m/s . (Take g = 10 m/s ^2 )

Step-by-step solution

Let the initial speed of the balls be u . When a ball is thrown vertically upwards with speed u , it goes up, reaches its maximum height, and returns to the level of the tower. The time taken for this upward and downward journey back to the release point is t = 2u g . Once it returns to the release point, it is moving downwards with the same speed u , which is exactly the same state as the ball thrown vertically downwards initially. Therefore, the difference in the time taken by the two balls to reach the ground is