an 80 - kg hiker climbs to the top of a tall hill and builds up 470,000 j of gravitational potential energy…

Explanation:

Step1: Recall potential - energy formula

The formula for gravitational potential energy is $U = mgh$, where $U$ is the gravitational potential energy, $m$ is the mass, $g$ is the acceleration due to gravity ($g=9.8\ m/s^{2}$), and $h$ is the height. We need to solve for $h$, so we can re - arrange the formula to $h=\frac{U}{mg}$.

Step2: Substitute the given values

We know that $U = 470000\ J$, $m = 80\ kg$, and $g = 9.8\ m/s^{2}$. $h=\frac{470000}{80\times9.8}$. First, calculate the denominator: $80\times9.8 = 784$. Then, $h=\frac{470000}{784}\approx600$.

Answer:

600