Question

A person walks up the mountain and another person jogs up the mountain; assuming they weigh the same, what would be a) their potential energies when the reach the summit b) the average power they expend when they reach the summit?

Answer 1

a) We have a formula for potential energy, (P.E.) = m *g *h

where m = mass (or weight of the person in Kg), g = acceleration due to gravity (9.8 m/s²) and h = height of the mountain from the mean sea level

As the weight of both persons is the same then, the potential energy would be the same for each person i.e. = m*g*h

b) The average power spent by each person would be different because they have different speeds of moving i.e. one is walking and another is jogging.

Power = Work/time = (Force * displacement)/time = (mass * acceleration due to gravity ) * (displacement /time) = mass (m) * acceleration due to gravity (g) * speed of their movement (v) = m * g * v

where m = mass (or weight of the person in Kg), g = acceleration due to gravity (9.8 m/s²) and v = speed of their movement