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?

Question

Mathematics

Claire Newman

27 July, 10:17

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?

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Answers (1)

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Greta Harding · Answer 1

1.95 seconds or 2.06 seconds

(Depending on your acceleration value)

Step-by-step 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)