A plane A is flying horizontally in direction 37° North of East. Another plane B is moving in East direction at 800 km/hr. Passengers in plane B see plane A moving in a direction 53° North of West. Wh

Question

A plane A is flying horizontally in direction 37° North of East. Another plane B is moving in East direction at 800 km/hr. Passengers in plane B see plane A moving in a direction 53° North of West. What is the true velocity of A?

TestHub · Accepted Answer

Resolve plane A's speed V into east and north components:

$V_{x} = V cos 3 7^{\circ} = \frac{4}{5} V, V_{y} = V sin 3 7^{\circ} = \frac{3}{5} V$

Plane B moves east at 800 km/h. Its view of A is 53° north of west:

$\frac{3 V /5}{800 - 4 V /5} = tan 5 3^{\circ} = \frac{4}{3}$

$9 V = 16000 - 16 V$

$V = 640 km/h$

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