v=((p)/(0.015))^(1)/(2) can be used to approximate the wind speed v in miles per hour given the power P measured in watts. How fast would the wind need to be to produce 150 watts of power? How much power would be generated by a steady 5 mph wind?

Question

v=((p)/(0.015))^(1)/(2) can be used to approximate the wind speed v in miles per hour given the power P measured in watts. How fast would the wind need to be to produce 150 watts of power? How much power would be generated by a steady 5 mph wind?

Answer 1

1. **Wind speed for 150 watts of power:**We are given the formula v = (p/0.015)^(1/2) and the power P = 150 watts. We need to find the wind speed, v.Substitute P = 150 into the formula:v = (150/0.015)^(1/2)v = (10000)^(1/2)v = 100 mphTherefore, the wind speed needs to be 100 mph to produce 150 watts of power.2. **Power generated by a 5 mph wind:**We are given the formula v = (p/0.015)^(1/2) and the wind speed v = 5 mph. We need to find the power, P.First, square both sides of the equation to get rid of the square root:v^2 = p/0.015Now, substitute v = 5:5^2 = p/0.01525 = p/0.015Now, multiply both sides by 0.015 to solve for p:p = 25 * 0.015p = 0.375 wattsTherefore, a steady 5 mph wind would generate 0.375 watts of power.

Question

v=((p)/(0.015))^(1)/(2) can be used to approximate the wind speed v in miles per hour given the power P measured in watts. How fast would the wind need to be to produce 150 watts of power? How much power would be generated by a steady 5 mph wind?

Solution

Answer