Question

consider a system of a cliff diver and the earth. the gravitational potential energy of the system decreases by 24,500 j as the diver drops to the water from a height of 30.0 m. determine her weight in newtons.

Explanation:

Step1: Recall potential - energy formula

The gravitational potential - energy formula is $U = mgh$, where $U$ is the gravitational potential energy, $m$ is the mass, $g$ is the acceleration due to gravity ($g\approx9.8\ m/s^{2}$), and $h$ is the height. The change in gravitational potential energy $\Delta U$ is related to the weight $W$ of the object by $\Delta U=W\times h$ (since $W = mg$).

Step2: Solve for weight

We know that $\Delta U = 24500\ J$ and $h = 30.0\ m$. Rearranging the formula $\Delta U=W\times h$ to solve for $W$, we get $W=\frac{\Delta U}{h}$.
Substitute the given values: $W=\frac{24500\ J}{30.0\ m}$.
$W = 816.67\ N$.

Answer:

$816.67$