Question

The function y = -16^2 + 486 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take to hit the ground? Round to the nearest hundredth of a second.

A.) 7.79 seconds
B.) 0.25 seconds
C.) 5.51 seconds
D.) 11.02

Answer 1

The function is
`y=f(t)=-16t^2+486`


for example, at time t=2s , the height y of the stone is found as follows:


`y=f(2)=-16\cdot 2^2+486=-16\cdot4+486=-64+486=422 (ft)`



When the ball hits the ground, the height y, becomes 0.

So we solve:


`0=-16t^2+486\\\\16t^2=486\\\\t^2=\displaystyle{(486)/(16)=30.375`



`t=√(30.375)\approx5.51`

Answer: C. 5.51 seconds