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A creature on the moon throws a rock off a cliff. The height of the rock above the surface of the moon, in meters, t seconds after it is thrown is given by h(t)=-t^2 +8t+10. When does the rock hit the surface of the moon?

 Jun 6, 2022
 #1
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When it hits the surface, the height = 0...so

 

-t^2  + 8t + 10  = 0

 

Use the quad formula

 

-8  ±  sqrt [ 8^2 -  4 * -1 * 10 ]                   -8 ± sqrt [ 104]           -8 ± 2sqrt (26)

_______________________  =             _____________  =   _____________  = 

           2 (-1)                                                      -2                                -2

 

4 -sqrt (26) sec  (reject)  or

 

4  + sqrt (26)sec ≈   9.1 sec

 

 

cool cool

 Jun 6, 2022
edited by CPhill  Jun 6, 2022

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