Question

It takes 23 seconds to hoist a rescue diver of mass 80 kg from the ocean surface to a helicopter hovering 23.9 meters above the ocean surface using a motor-driven cable. How much power (in Watts) was supplied by the motor to hoist the diver into the helicopter at a constant speed

Answer 1

Answer:

840 W

Explanation:

The energy expended in hoisting the diver up is given by

$E = mgh$

m is the mass of the diver, g is the acceleration due to gravity and h is the height.

Using the values in the question and taking g as 9.8 m/s²,

$E = (80\text{ kg})\times (9.8\text{ m/s}^2)\times (23.9\text{ m}) = 18737.6\text{ J}$

The power is given by

$P = \dfrac{E}{t}$

t is the time.

Hence,

$P = \dfrac{18737.6\text{ J}}{23\text{ s}} = 841.678\ldots \text{ W}\approx 840\text{ W}$