A ball is thrown straight upward in the air at a speed of 18.0 m/s. Ignore air r

Question

A ball is thrown straight upward in the air at a speed of 18.0 m/s. Ignore air resistance. (a) What is the maximum height the ball will reach? (b) What is the speed of the ball when it reaches 2.90 m? (c) How long will it take to reach 2.90 m above its initial position on the way up? (d) How long will it take to reach 2.90 m above its initial position on its way down?

A) 16.4 m, 16.2 m/s, 0.168 s, 3.0 s

B) 16.5 m, 16.3 m/s, 0.169 s, 3.5 s

C) 16.0 m, 16.3 m/s, 0.179 s, 3.9 s

D) 17.5 m, 16.3 m/s, 0.160 s, 4.5 s

Explanation / Answer

B)16.5 m, 16.3 m/s, 0.169 s, 3.5 s

explanation

a) 2 g h = v^2

h = 18^2 / (2 * 9.8) = 16.53m

b) 2 * (-9.8) * 2.9 = v^2 - 18^2

v = 16.34m/s

c) s = ut + 0.5 * gt^2

2.9 = 18t - 4,9t^2

solving the quadratic we get

taking the first root

t = 0.1688s

d) take the second root of the quadratic in part c)

t = 3.50s

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