"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?"

Question

I have no idea how to solve this, steps and explanations would be amazing.

Answer 1

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

Answer 2

W we tp