Posted by **BILLY** on Wednesday, December 5, 2012 at 12:12pm.

An airplane flies due north at 200 km/h relative to the air. There is a wind blowing at 70 km/h to the northeast relative to the ground. What are the plane's speed and direction relative to the ground?

- physic -
**Elena**, Wednesday, December 5, 2012 at 3:49pm
v=200 km/h, v₀= 70 km/h,

Angle that make v and v₀ is 45° =>

An angle α in cosine law is

α (360°-2•45°)/2 =135°

Cosine law:

V=sqrt(v²+v₀²-2vv₀cos α)=

=sqrt[40000+4900-2•200•70•(-0.707)]=254 km/h

Projections:

x: v•cos90 +v₀cos45° =254cosβ

y:vsin90+ v₀sin45°=254sinβ

0.707•70 =254 cosβ

200+0.707•70 = 254 sinβ

49.49 =254 cosβ

249.49 =254 sinβ

sinβ/cosβ=tanβ =249.49/49.49 = 5.04

β =tan⁻¹5.04 = 78.8° (northwest)

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