Question

If a paper plane is thrown from the top of a 147-foot cliff into the water below, the height of the plane at any given time can be determined by the formula h = -3t² + 147, where h is the height of the plane at t seconds. After how many seconds will the plane be at a height of exactly 20.25 feet?a. 7 seconds b. -6.5 seconds c. 6.5 seconds d. 7 seconds

Answer 1

c. 6.5 seconds.

Explanation:

We have been given that a a paper plane is thrown from the top of a 147-foot cliff into the water below, the height of the plane at any given time can be determined by the formula
`h = -3t^2+147`, where h is the height of the plane at t seconds.

To find the time, when plane will be at a height of exactly 20.25 feet, we will substitute
`h=20.25` in our given formula and solve for t as:

`20.25= -3t^2+147`

`-3t^2+147=20.25`

`-3t^2+147-147=20.25-147`

`-3t^2=-126.75`

`(-3t^2)/(-3)=(-126.75)/(-3)`

`t^2=42.25`

Take square root of both sides:

`t=\pm √(42.25)`

`t=\pm 6.5`

Since time cannot be negative, therefore, the plane will be at a height of exactly 20.25 feet after 6.5 seconds and option 'c' is the correct choice.