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?

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