Question

A 63 kg gymnast climbs 15 m up a vertically hanging rope. He completed the distance in 70 seconds. How much power did his body output to achieve the climb? A) 13.5 Watts B) 132.2 Watts C) 9,261 Joules Eliminate D) 648,270 Watts

Answer 1

Let's take a look at your given first:

mass = 63kg
distance = 15m
t = 70 seconds

Power is the amount of work done within a span of time. If placed in a formula it is written as:

$P = \frac{work}{time}$

However, if you use this formula, you will see that you have 2 unknowns. This can easily be worked out if you combine formulas into one. 

First you will need to know the formula of Work, which is:

Work = Force x Distance

But because you do not know the Force yet, this will not be applicable just yet. Force according to the second law of motion is the product of mass and acceleration or:

F = mass x acceleration

Now that you know these three formulas you can combine them into one:

$P = \frac{work}{time}$  or $\frac{Force x distance}{time}$

Because Force is unknown as well, we will substitute the Force with its formula and the equation will now look like this:

$P = \frac{mad}{time}$

Where: P = power
             m = mass
             a = acceleration
             d = distance
             t  = time

So now you have your new formula to use.

Going back to your given, you might have thought that you do not have acceleration, but you do. When it comes to vertical motion, there is a constant acceleration present that is applied by the gravity of the Earth, which is 9.8m/s². This is the acceleration you will use, given that he is moving vertically.

Now we can input what we know and solve for what we need:

$P = \frac{mad}{time}$
$P = \frac{63kgx 9.8m/s² x 15m }{70s}$
$P = \frac{9,268kg.m²/s² }{70s}$
$P = 132.2 kg.m²/s or 132.2 Watts$

With that, your answer is letter B.