Question

A diver is on the diving platform at Wonder Mountain in Canada’s Wonderland. She jumps up and dives into the water at the base of the mountain. The equation is d = -3t^2 + 6t + 45

At what time is she 36 m above the water?

When is she less than 21 m from the water?

Answer 1

-3t^2 + 6t + 45 = 36
-3t^2 + 6t + 9 = 0
t^2 - 2t - 3 = 0
(t-3)(t+1) = 0

t=3 or t=-1 , but we know t >= 0
so at 3 seconds she is 36 m above the ground

-3t^2 + 6t + 45 < 21
t^2 - 2t -8 > 0
(t-4)(t+2) > 0
t > 4 or t < -2

let's see when she hits the water.
-3t^2 + 6t + 45 = 0
t^2 - 2t + 15=0
(t-5)(t+3) = 0
t = 5

So she will be between 21 m and the ground
from second 4 and 5 seconds