Question

Brian "bicycle kicked" a soccer ball up from a height of 4ft off the ground with an initial upward velocity of 34 feet/sec. As the ball was coming down, Mike jumped up and at 8 ft off the ground, headed it into the goal and win the game. How long did it take for the ball to come down and reach Mike's head?

Answer 1

1.95 seconds or 2.06 seconds

(Depending on your acceleration value)

Explanation:

s = ut + 0.5at²

u = 34 ft/s

a = -10 m/s² = -32.8084 ft/s²

s = 8-4 = 4 ft

4 = 34t + ½(-32.8084)t²

4 = 34t - 16.4042t²

16.4042t² - 34t + 4 = 0

t = 1.946, 0.125

Mike catches the ball the second time it was at a height of 8ft.

Do t = 1.95 s

If you use a = 32.17405 ft/s²,

t = 2.05655765 (2.06 seconds in 3 sf)