Question

A ball is thrown vertically upward from the top of a building with an initial velocity of 96 feet per second. The ball's h height after t seconds is given by the equation h = −16t2 + 96t + 100. How long will it take for the ball to hit the ground? (to the nearest tenth of a second) A) 5.9 seconds B) 6.3 seconds C) 6.9 seconds D) 7.2 seconds

Answer 1

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Answer 2

C) 6.9 seconds

Explanation:

h = -16t² + 96t + 100

When the ball hits the ground, h = 0.

0 = -16t² + 96t + 100

0 = 4t² − 24t − 25

Solve with quadratic formula:

t = [ -b ± √(b² − 4ac) ] / 2a

t = [ -(-24) ± √((-24)² − 4(4)(-25)) ] / 2(4)

t = [ 24 ± √(576 + 400) ] / 8

t = (24 ± √976) / 8

t = (24 ± 4√61) / 8

t = (6 ± √61) / 2

t = -0.91 or 6.9

Since t must be positive, t = 6.9 seconds.