A ball rolls off the top of a stairway with horizontal velocity u . The steps are 0 . 1 m high and 0 . 1 m wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be x m s - 1 , where x = _______ [use g = 10 m s - 2 ].

Step-by-step solution

The ball needs to just cross 4 steps to just hit 5 th step Therefore, horizontal range R = 4 × 0 . 1 m = 0 . 4 m The formula to calculate the horizontal range is given by R = u t . . . 1 Similarly, the vertical height covered by the ball is given by h = 1 2 g t 2 . . . 2 From equations (1) and (2), it follows that 4 × 0 . 1 = 1 2 g t 2 ⇒ 0 . 4 = 1 2 g 0 . 4 u 2 ⇒ u 2 = 2 ⇒ u = 2 m s - 1 Therefore, x = 2 .