A model rocket is launched vertically from a platform 64 feet above the ground. The height the rocket reaches during the flight is modeled by the equation s (t) = - 16t2 48t 64, where s is the height of the rocket and t is the time in seconds since the launch. After how many seconds will the rocket hit the ground?

Question

Mathematics

Kylan Bridges

25 March, 05:39

A model rocket is launched vertically from a platform 64 feet above the ground. The height the rocket reaches during the flight is modeled by the equation s (t) = - 16t2 48t 64, where s is the height of the rocket and t is the time in seconds since the launch. After how many seconds will the rocket hit the ground?

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Answers (1)

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Ayla Crawford · Answer 1

At ground level, the height is = 0. Therefore, s (t) = 0.

0 = - 16t2 + 48t + 64

Divide both sides by - 16.

0 = - 16 (t2 - 3t - 4)

We are left with this equation: 0 = t2 - 3t - 4

Factor out.

0 = (t - 4) (t+1)

We solve each separately.

0 = (t-4)

t = 4

0 = (t+1)

t = - 1

We are left with two answers but time cannot be negative so t = 4 seconds.