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Calculate the man's mass. Round your answer to the nearest whole number.

A man climbs a wall that has a height of 8.4 meters and gains a potential energy of 4,620 joules.

(Use [tex]\( PE = m \times g \times h \)[/tex], where [tex]\( g = 9.8 \, N/kg \)[/tex].)

His mass is about [tex]\(\square\)[/tex] kilograms.

Sagot :

GinnyAnswer
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.
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