SOLUTION: A rock is thrown upward with a velocity of 14 meters per second from the top of a 35 meter high cliff, and it misses the cliff on the way back down. When will the rock be 3 meters

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Question 1203448: A rock is thrown upward with a velocity of 14 meters per second from the top of a 35 meter high cliff, and it misses the cliff on the way back down. When will the rock be 3 meters from ground level? Round your answer to two decimal places.
Answer by ikleyn(52915) About Me  (Show Source):
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A rock is thrown upward with a velocity of 14 meters per second from the top of a 35 meter high cliff,
and it misses the cliff on the way back down. When will the rock be 3 meters from ground level?
Round your answer to two decimal places.
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The function describing the height over the base of the cliff is

    h(t) = -5t^2 + 14t + 35.


The rock will be 3 meters from ground level when h = 3.


So, to find the relevant time t, you should solve this equation

    -5t^2 + 14t + 35 = 3.


Simplify

    -5t^2 + 14t + 32 = 0

     5t^2 - 14t - 32 = 0


and find t using the quadratic formula

    t = %2814+%2B-+sqrt%28%28-14%29%5E2+-4%2A5%2A%28-32%29%29%29%2F%282%2A5%29 = %2814+%2B-+28.91366459%29%2F10.


Use the positive root and reject the negative one.


ANSWER.  t = %2814+%2B+28.91366459%29%2F10 = 4.29 seconds  (rounded).

Solved.

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