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

Answer:

c. 6.5 seconds.

Step-by-step 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:

$20.25= -3t^2+147$

$-3t^2+147=20.25$

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

$-3t^2=-126.75$

$\frac{-3t^2}{-3}=\frac{-126.75}{-3}$

$t^2=42.25$

Take square root of both sides:

$t=\pm \sqrt{42.25}$

$t=\pm 6.5$

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.