1. The pressure P of wind on a sail varies jointly as the area A of the sail and the square of the velocity V of the wind. The pressure on a square foot is 1 pound when the velocity is 16 miles per hour. Find the velocity of the wind when the pressure on a square yard is 36 pounds?
1. Answer:32 miles per hour.
Solution:We have P = kAV2, where k is a constant. It is given that P = 1 when A = 1 and V = 16. Hence, 1 = k(1)(16 x 16) and so k = 1/256. Thus 36 = (1/256) x 9 x V2. So V2 = 1024 giving V = 32 miles per hour. (Remember a square yard is 9 times a square foot)
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