Question

What is average Power generated by a $70\,kg$ mountain climber who climbs a summit of height $325\,m$ in $95.0\min $?
A. $39.1\,W$
B. $54.6\,W$
C. $25.5\,W$
D. $69.0\,W$
E. $88.4\,W$

Answer 1

Hint:Before answering the question let us have some idea about mechanics. Mechanics is a branch of physics that studies how bodies move as they are exposed to forces or displacements, as well as the impact of the bodies on their surroundings.

Complete step by step answer:
We may describe power as the rate at which work is completed, or the amount of work completed in a given amount of time \[{\text{ }}Watt{\text{ }}\left( W \right)\], or \[joules{\text{ }}per{\text{ }}second{\text{ }}\left( {J/s} \right)\], is the SI unit of electricity. \[Horsepower{\text{ }}\left( {hp} \right)\], which is roughly equivalent to \[745.7{\text{ }}watts\], is often used to describe the power of motor vehicles and other devices.

The rate at which work is done on an object is known as power. Power is a metric that is measured over a period of time. Which has everything to do with how quickly a job is completed. The formula for calculating power is given below.
\[\text{Work}/\text{Time}= \text{Power}\]

Average power: The total energy consumed divided by the total time taken is what we call average power. In simple terms, average power is defined as the average amount of work or energy converted per unit of time.

As we all know, the rate of work done is measured in power, so when a climber ascends, the work is done against gravity. As a result, we can conclude that work done is
$W = mgh$
$\Rightarrow W = \left( {70} \right) \times \left( {9.81} \right) \times \left( {325} \right)$
$\Rightarrow W = 223177.5\,J$
Now we know how long it took him to get to that spot, which is given as
$t = 95\min $
$\Rightarrow t = (95 \times 60)\sec $
$\Rightarrow t = 5700\sec $
As a result, power is given as:
$P = \dfrac{W}{t}$
$\Rightarrow P = \dfrac{{223177.5}}{{5700}}$
$\therefore P = 39.1\,W$

Hence, the correct answer is option A.

Note:The joule (J) is the metric unit of function and energy calculation. The belief that work and energy are linked and can be transformed into one another is reinforced by measuring them with the same unit.