# Calculus/Vectors

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An airplane heads due south with an air speed of 480km/h. Measurements made from the ground indicate that the plane's ground speed is 528km/h at 15 degrees east of south. Calculate the wind speed.

• Calculus/Vectors -

make a sketch with O the origin
OP = 480 and south along the y-axis.
draw OR as the resultant of length 528 and angle POR = 15°
Complete the parallogram with OQ =PR and QR = OP

by cosine law:
PR^2 = 480^2 + 528^2 + 2(480)(528)cos15°
PR = 139.9125

So the wind speed is 139.9 km/h

• Calculus/Vectors -

so by using that formula for cosine i somehow still can't get the right answer :(

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