Question

An old man and a young boy both of mass 50 kg climb up the same height. While the old man climbs up in 25 seconds, the Boy climbs up in 15 seconds calculate the ratio of the:
(A) work done by them and
(B) Their power.

Answer 1

Hint: We can use the results from work done to calculate the ratio of the power. Since the displacement of the man and the boy is the same so we can say that the work done by both is equal.
Formula used: In the solution we will use the formula of work done which is
\[Work\,Done = mgh\]
Where,
\[m\] is the mass
\[g\] is the acceleration due to gravity
\[h\] is the height
And,\[Power = \dfrac{{work\,done}}{{time}}\]

Complete step by step solution:
We have
\[m = 50kg\]
And we know the value of acceleration due to gravity that is
\[g = 9.8\dfrac{m}{{{s^2}}}\]
Substituting values of mass and acceleration due to gravity in the work done formula:
\[Work\,Done = mgh\]
\[ \Rightarrow work\,done = 50 \times 9.8 \times h\]
Same work is done by old man and the young man
So the ratio of the work done by them is \[1:1\]
Now we have
\[Power = \dfrac{{work\,done}}{{time}}\]
The power of the boy \[ = \dfrac{{500h}}{{15}}\]
Power of the old man \[ = \dfrac{{500h}}{{25}}\]
Therefore, power of the old man : power of the boy = \[\dfrac{{500h}}{{25}}:\dfrac{{500h}}{{15}}\]
Which is \[3:5\]

The ratio of their powers is \[3:5\]

Additional information: Work done is the energy transferred to or from the object by applying force along a displacement. The unit of work done is joule. Work done is also a scalar quantity.
\[work\,done = Force \times displacement\]
Power is the amount of energy transferred per unit time. The unit of power is watts which is equal to one joule per second. It is a scalar quantity
\[Power = \dfrac{{work\,done}}{{time}}\]

Note: While finding the ratio we can either find the ratio of power of old man with respect to the power of the boy or the other way round. Both the answers will be correct as long as we mention how we calculated the ratio.