# Vectors

A plane is steering east at a speed of 240km/h. What is the ground speed of the plane if the wind is from the northwest at 65km/h. What is the plane's actual direction?

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1. speed relative to ground: 240E+65*cos45E+65*sin45S
combine like directions, then directionactual= arctan(S/E) south of East.

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bobpursley
2. resultant = 240(1,0) + 65(cos315, sin315)
= (240,0) + (45.962, -45.962)
= (285.962, -45.962)

|resultant| = √(285.962^2 + (-45.962^2 )
= 289.63 km/h
angle: tanØ = -45.962 ÷ 285.962 = ....
Ø = 350.9°°
or S 80.9*° E

or by cosine law:
R^2 = 240^2 + 65^2 - 2(240)(65)cos135°
= 83886.73..
R = 289.63
now use the Sine Law to find the angle

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