The height of a rock thrown off a cliff can be modeled by h=-16t^2-8t+120, where h is the height in feet and t is time in seconds. how long does it take the rock to reach the ground?

The rock hits the ground after 4 seconds.


Here is the work in how you can find this answer...:


The height, h, of an object thrown upward from an initial height, H, with an initial velocity, Vo, is given by the function h as a function of time, t:

h(t) = -16t^2 + Vot + H

Since Vo = 48 ft/sec and H 64 ft, then: 

h(t) = -16t^2 + 48t + 64

You want to know at what time, t, will the rock hit the ground (h = 0). Set the above function = 0. 

-16t^2 + 48t + 64 = 0

Solve this quadratic equation for t. First, factor -16.

-16 ( t^2 - 3t -4 ) = 0

Apply the zero products principle.

t^2 - 3t - 4 = 0

Factor.

( t - 4 )( t + 1 )

Again, apply the zero products principle.

t - 4 = 0 and/or  t + 1 = 0

If t - 4 = 0, then t = 4 seconds

If t + 1 = 0, then t = -1 second...Discard this solution as negative time is not meaningful in this problem.

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OVERALL = THE ROCK HITS THE GROUND AFTER 4 SECONDS
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Idon’t see the picture