Question

A 45.7 kg woman starts from rest at the bottom of a flight of stairs that has

a total height of 2.54 meters. She reaches the top of the stairs
in 5.00 seconds. How much power does she generate if she is moving at
2.63 m/s at the top of the stairs? Use g = 9.8 m/s2, and only include 3
numbers in your answer.

Answer 1

The power generated by the woman is 259 W

Step-by-step explanation:

Given;

mass of the woman, m = 45.7 kg

initial velocity of the woman, u = 0

total height ascended by the woman, h = 2.54 m

time of the woman's motion, t = 5.0 s

final velocity of the woman, v = 2.63 m/s

acceleration due to gravity, g = 9.8 m/s²

The potential energy of the woman due to the height she ascended;

P.E = mgh

P.E = 45.7 x 9.8 x 2.54

P.E = 1137.564 J

The kinetic energy of the woman due to her final velocity;

K.E = ¹/₂mv²

K.E = ¹/₂ x 45.7 x (2.63)²

K.E = 158.051 J

The total mechanical energy of the woman at the top of the stairs;

M.E = P.E + K.E

M.E = 1137.564 J + 158.051 J

M.E = 1295.615 J

The power generated by the woman;

Power = Energy/time

Power = 1295.615 J / 5 s

Power = 259.123 W

Power = 259 W