The wind pressure on the sails of a sailboat varies proportionally with the area of the sails and the square of the wind speed. The formula to calculate this is:
p = kA Ã v2
Where:
- p is the wind pressure
- k is the constant of proportionality
- A is the area of the sails
- v is the wind speed
To determine the wind speed when the pressure on a square yard is 36 pounds, we can follow these steps:
Calculation:
Given:
- Pressure on a square foot = 1 pound
- Wind speed = 16 miles per hour
Using the given information, we can establish the equation:
1 lb/ft2 = k à 1 ft2 à (16 mph)2
Next, calculate the pressure when the area is converted to square yards:
- Pressure on a square yard = 36 pounds
- 1 yard = 3 feet
Therefore,
- Pressure on a square foot = 36 lb/yard2 Ã (1 yard / 3 feet)2 = 4 lb/ft2
- Area of a square yard = 1 yard2 Ã (3 feet / yard)2 = 9 ft2
Now, we have:
4 lb/ft2 = k à 9 ft2 à v2
By dividing this equation with the previous equation, we can eliminate the constant, k, and solve for the wind speed:
v2 = 4 Ã (16 mph)2 / 9
v = 2 Ã 16 mph / 3
v â 10.7 mph â 11 mph
Therefore, the wind speed when the pressure on a square yard is 36 pounds is approximately 11 mph.