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 2 of 3: how many seconds did it take for the ball to reach a height of 256 feet above the ground?

Explanation:

Step1: Substitute height value

Substitute $h = 256$ into $h=400 - 16t^{2}$, getting $256=400 - 16t^{2}$.

Step2: Rearrange the equation

Rearrange to get $16t^{2}=400 - 256$. Then $16t^{2}=144$.

Step3: Solve for $t$

Divide both sides by 16: $t^{2}=\frac{144}{16}=9$. Take the square - root of both sides. Since $t\geq0$ (time can't be negative in this context), $t = 3$.

Answer:

3