To calculate the man's mass based on the given potential energy, height, and gravitational constant, we can use the formula for potential energy:
[tex]\[
PE = m \times g \times h
\][/tex]
Given:
- Potential energy ([tex]\(PE\)[/tex]) = 4620 joules
- Acceleration due to gravity ([tex]\(g\)[/tex]) = 9.8 N/kg
- Height ([tex]\(h\)[/tex]) = 8.4 meters
We need to solve for the man's mass ([tex]\(m\)[/tex]). Rearranging the formula to solve for [tex]\(m\)[/tex]:
[tex]\[
m = \frac{PE}{g \times h}
\][/tex]
Substituting the known values:
[tex]\[
m = \frac{4620}{9.8 \times 8.4}
\][/tex]
When we calculate this, we find:
[tex]\[
m \approx 56.12244897959183 \text{ kg}
\][/tex]
Rounding to the nearest whole number:
[tex]\[
m \approx 56 \text{ kg}
\][/tex]
Therefore, the man's mass is about 56 kilograms.
