Question

the formula $v = \sqrt{2gh}$ gives the velocity $v$, in feet per second, of an object when it falls $h$ feet accelerated by gravity $g$, in feet per second squared. if $g$ is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 160 feet per second.
$h = \square$ ft

Explanation:

Step1: Rearrange formula for h

Square both sides: $v^2 = 2gh$, so $h=\frac{v^2}{2g}$

Step2: Substitute given values

$v=160$, $g=32$: $h=\frac{160^2}{2\times32}$

Step3: Calculate numerator and denominator

$160^2=25600$, $2\times32=64$

Step4: Compute final value

$h=\frac{25600}{64}=400$

Answer:

$h=400$ ft