Question

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?

Answer 1

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)

Answer 2

Umm lol no