Question

an 80-kg hiker climbs to the top of a tall hill and builds up 470,000 j of gravitational potential energy. how high did the hiker climb? round the answer to the nearest hundred.
meters

Explanation:

Step1: Recall the formula for gravitational potential energy

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

Step2: Substitute the given values into the formula

We know that $PE = 470000\ J$, $m = 80\ kg$, and $g = 9.8\ m/s^2$. Substituting these values into the formula for $h$, we get $h=\frac{470000}{80\times9.8}$.

Step3: Calculate the denominator first

Calculate $80\times9.8 = 784$.

Step4: Calculate the height

Now, divide $470000$ by $784$: $h=\frac{470000}{784}\approx599.49$.

Step5: Round to the nearest hundred

Rounding $599.49$ to the nearest hundred, we look at the tens digit (9), which is greater than or equal to 5, so we round up the hundreds digit. $599.49$ rounded to the nearest hundred is $600$.

Answer:

600