Verified answer

wind resistance (R) varies jointly as an object's surface area (s) and velocity (v). If an object travelling 40 mile per hour with a surface area of 25 square feet experience a wind resistance of 225 Newtons, how fast must a car with 40 square feet of surface area travel in order to experience a wind resistance of 270 newtons.

Given: Resistance (R), Surface area (S), Velocity (V)

• Resistance - 225N, 270N
• Surface area - 25 square feet, 40 square feet
• Velocity - 40 mph, ?

Translation (joint variation):

• r = ksv

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• r = 225, s = 25, v = 40
• 225 = k • 25 • 40
• 225 = k • 1000
• 225/1000 = k
• 9/40 = k

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• r = 270, s = 40, v = ?
• 270 = 9/40 • 40 • v
• 270 = 9v
• 270/9 = v
• 30 = v

• The car will travel at 30 miles per hour.