Question

How fast would a 130kg person have to run in (m/s) in order to have the same energy as that of a 100 W light bulb uses per hour.

Answer 1

74.4 m/s

Step-by-step explanation:

The power of the light bulb is

P = 100 W

We can find the energy used by the light bulb in one hour by using the equation

`E=Pt`

where

t = 1 h = 3600 s is the time interval

Substituting,

`E=(100)(3600)=360,000 J`

Now, we want the person to have the same energy. Since he is running, we are talking about kinetic energy, which is given by

`K=(1)/(2)mv^2` (1)

where

m = 130 kg is the mass of the person

v is his speed

We said that his kinetic energy must be equal to the energy used by the bulb:

K = 360,000 J

Therefore, we can rearrange eq.(1) to find what speed the man should have:

`v=\sqrt{(2K)/(m)}=\sqrt{(2(360,000))/(130)}=74.4 m/s`