Question

a ball is dropped from the top of a building that is known to be 400 feet high. the formula for finding the height of the ball at any time is h = 400 - 16t², where t is measured in seconds. step 3 of 3: how many seconds did it take for the ball to fall 144 feet?

Explanation:

Step1: Find remaining height

The building is 400 feet high and the ball falls 144 feet. So the remaining height $h$ is $400 - 144=256$ feet.

Step2: Substitute into formula

We know the formula $h = 400-16t^{2}$. Substitute $h = 256$ into it, getting $256=400 - 16t^{2}$.

Step3: Rearrange the equation

First, move the terms around: $16t^{2}=400 - 256$. Then $16t^{2}=144$.

Step4: Solve for $t$

Divide both sides by 16: $t^{2}=\frac{144}{16}=9$. Take the square - root of both sides. Since $t>0$ (time cannot be negative in this context), $t = 3$.

Answer:

3