Asked by Emily
"A rock is dropped from the edge of a 180 m cliff. the function f(x) = -5t^2 - 5t + 180 gives the height of the rock, h(t), in meters t seconds after it was released. How long does it take for the rock to reach a ledge 80 m above the base of the cliff?"
I have no idea how to solve this, steps and explanations would be amazing.
I have no idea how to solve this, steps and explanations would be amazing.
Answers
Answered by
Steve
well, since f(t) is the height of the rock at time t, just set it to 80 and solve for t:
-5t^2 - 5t + 180 = 80
5t^2 + 5t - 100 = 0
t^2 + t - 20 = 0
(t+5)(t-4) = 20
t=4
check:
f(4) = -5(16)-5(4)+180 = 80
-5t^2 - 5t + 180 = 80
5t^2 + 5t - 100 = 0
t^2 + t - 20 = 0
(t+5)(t-4) = 20
t=4
check:
f(4) = -5(16)-5(4)+180 = 80
Answer
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