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 [tex]h = -3t^2+147[/tex], 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 [tex]h=20.25[/tex] in our given formula and solve for t as:
[tex]20.25= -3t^2+147[/tex]
[tex]-3t^2+147=20.25[/tex]
[tex]-3t^2+147-147=20.25-147[/tex]
[tex]-3t^2=-126.75[/tex]
[tex]\frac{-3t^2}{-3}=\frac{-126.75}{-3}[/tex]
[tex]t^2=42.25[/tex]
Take square root of both sides:
[tex]t=\pm \sqrt{42.25}[/tex]
[tex]t=\pm 6.5[/tex]
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.
