Answer to Question #154376 in Classical Mechanics for John smith

Question

a 55kg student climbs 5.6m up a rope gym class at a constant speed of 1.6 m/s . Determine the power exerted by the student with and without determining the time taken. 

Answer 1

a) Let's determine the power exerted by the student with determining the time taken:

$$P=\dfrac{W}{t}=\dfrac{mgh}{\dfrac{s}{v}},$$ $$P=\dfrac{55\ kg\cdot 9.8\ \dfrac{m}{s^2}\cdot 5.6\ m}{\dfrac{5.6\ m}{1.6\ \dfrac{m}{s}}}=862.4\ W.$$

b) Let's determine the power exerted by the student without determining the time taken:

$$P=Fv=mgv=55\ kg\cdot 9.8\ \dfrac{m}{s^2}\cdot 1.6\ \dfrac{m}{s}=862.4\ W.$$