Question

The pilot of an airplane notes that the compass indicates a heading due west. The airplane's speed relative to the air is 110 km/h. The air is moving in a wind at 29.0 km/h toward the north. Find the velocity of the airplane relative to the ground.

Magnitude _______	km/h
Direction ______

Answer 1

Answer 2

This question does not involve calculus. It requires vector algebra.

Taking the ground as the frame of reference, the velocity vector of the plane points due west, whereas the velocity vector of the wind is (0, 29).

Relative speed = plane - wind
= (-x, 0) - (0, 29)
= (-x, -29).

If this vector is to have a magnitude of 140km/h, then x^2 + 841= 12100

x = sqrt(11259)

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