SOLUTION: The power P obtained a windmill is directly proportional to the cube of the wind speed s. a) Write an equation that expresses this variation. b) Find the constant of proportion

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Question 1023112: The power P obtained a windmill is directly proportional to the cube of the wind speed s.
a) Write an equation that expresses this variation.
b) Find the constant of proportionality for a windmill that produces 96 watts of power when the wind is blowing at 20 mi/hr.
c) How much power will this windmill produce if the wind speed increases to 30 mi/hr.
Found 2 solutions by josgarithmetic, god2012:
Answer by josgarithmetic(39616) (Show Source):
You can put this solution on YOUR website!
k is a proportionality constant.

Solve for the konstant in the formula.

You can find the value for k if you know a set of values for s and P.

That is how this works.

Answer by god2012(113) (Show Source):
You can put this solution on YOUR website!
Given : P is directly proportional to cube of windspeed S
P ∝ s⌃3
= >
P = k*s⌃3 , where k is a constant
a) k = {P/s⌃3}
b) speed s = 20 mi/hr
Power P = 96W
k = {96 / 20⌃3} = 96/8000 = 0.012
k = 0.012
c) s = 30
k = 0.012
P = k*s⌃3 = 0.012*30⌃3 = 324
P = 324 W