Question

1. The center of mass of Tom is positioned 1.1m above the ground while he is standing in anatomical position. During a run, Tom’s average horizontal velocity is 2m/s. After he pushes off from the ground (a flat surface), his horizontal velocity is 2.5 m/s, while his vertical velocity is 0.5 m/s and his center of mass is positioned 1.15m above the ground. Find the following: a) the displacement of the center of mass vertically for take-off to the apex, b) the time it takes to reach the apex, c) assuming the landing height and take-off heights of the center of mass are the same, his range, and d) total time in the air.

Answer 1

his vertical speed at time t after pushoff is v = 0.5-9.8t
The apex is reached when v=0
so find t when v=0 to evaluate his apex height, h = 1.15+0.5t-4.9t^2

His range is just 2.5 * 2t (time down = time up)