William W. answered • 03/05/20
Experienced Tutor and Retired Engineer
Ten 100 kg who are at the top of a 40 m ski slope have a certain amount of energy - gravitation potential energy as referenced from the bottom of the hill. The equation of that potential energy is PE = mgh where "PE" is the potential energy, "m" is the mass, and "g" is the gravitational acceleration (9.81 m/s2) and "h" is the height above the reference (bottom of the hill). So, the energy they have is:
PE = mgh = (10)(100)(9.81)(40) = 392,400 joules.
Since they have that energy, and at the bottom of the hill they had none (h = zero so "mgh" is zero), bringing them up the hill must have required that much energy.
Power is energy per unit time. Watts are joules/second. So, since 2 minutes is 120 seconds, the power required was (392,400 joules)/(120 seconds) = 3,270 watts. Since there is only 1 significant figure in each of the given values, we round our answer to 1 sig fig to get 3000 watts.
