A rocket is launched into the air. The projectile motion of the rocket can be modeled using h (t) = 112t - 16t2, where t is the time since launch in seconds and h (t) is the height of the rocket at time t. When will the rocket be 196 feet in the air?

Question

Mathematics

Simone

19 March, 06:00

A rocket is launched into the air. The projectile motion of the rocket can be modeled using h (t) = 112t - 16t2, where t is the time since launch in seconds and h (t) is the height of the rocket at time t. When will the rocket be 196 feet in the air?

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Answers (1)

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Jair · Answer 1

H (t) = 112 t - 16 t²

When the rocket is 196 feet in the air:

196 = 112 t - 16 t²

16 t² - 112 t + 196 = 0 / : 4

4 t² - 28 t + 49 = 0

(2 t - 7) ² = 0

2 t - 7 = 0

2 t = 7

t = 7 : 2

t = 3.5 s

Answer: The rocket will be 196 feet in the air after 3.5 seconds.