Question

You are riding a roller coaster when a shoe falls off your foot. The function y=300−16t2 represents the height y (in feet) of the shoe t seconds after it falls off your foot. The shoe lands on the top of an 11-foot-tall building. After how many seconds does the shoe hit the building?

Answer 1

Time to land on 11ft is 4.25 seconds

Explanation:

Given

`y = 300 - 16t^2`

Required

Solve for t when height is 11ft

This implies that
`y = 11`

So: substitute 11 for y in
`y = 300 - 16t^2`

`11 = 300 - 16t^2`

Collect Like Terms

`16t^2 = 300 - 11`

`16t^2 = 289`

Express both sides as squares

`4^2 * t^2 = 17^2`

`(4t)^2 = 17^2`

Take square roots of both sides (ignore negative)

`4t = 17`

Solve for t

`t = (17)/(4)`

`t = 4.25`

Hence, time to land on 11ft is 4.25 seconds