Question

A football is kicked straight up in the air , it hits the ground 5.6 s later. What was the greatest height kicked reached by the ball? Assume it was kicked at ground level.

Answer 1

Answer: 38.5 m

Explanation:

1) Flight time = 5.6 s (given)

2) Ascending time = fligth time / 2 = 5.6s / 2 = 2.8 s

3) Vf = Vo - gt

Hmax ⇒ Vf = 0

⇒ 0 = Vo - gt ⇒ Vo = gt = 9.81m/s² (2.8s) = 27.5 m/s

4) H = Vot - gt² / 2

⇒ H = 27.5m/s(2.8s) - 9.81m/s² (2.8s)² / 2 = 77m - 38.5m = 38.5m

Answer: 38.5m

Answer 2

We'll just consider the down trip, from when it was at its highest point to when it hits the ground.  Initial velocity is 0 m/s, acceleration is 9.81 m/s^2 (gravity), and time is 5.6s.

One of the kinematic equations is d = (Vi)(t) + 0.5(a)(t^2).
Plugging it in gives us d = 0 + (0.5)(9.81)(5.6^2) = 153.8208 m.

Hope this helped!