Relative Motion prob,

Relative Motion prob, plz help

1. The problem statement, all variables and given/known data
A pilot of an plane has to get to a point 320 km due North in 1 hour. Ground Control reports inform that there is a cross wind of 80 km/h towards 37o South of West. What is the required heading pf the plane?


2. Relevant equations
VPE = VPW + VWE


3. The attempt at a solution

Horizontal component

VPE = VPW + VWE

0 = xcosᵝ - 80cos37
xcosᵝ = 80 cos37 --------------(1)

Vertical component

VPE = VPW + VWE

320 = xsinᵝ - 80 sin37
xsinᵝ = 80(4 +sin37) -------------(2)

Angle (heading angle)


(2)/(1)


tanᵝ = (4+sin37)/cos37 = (4 + 0.601)/0.7986 = 5.761

ᵝ = tan-1(80.15)


Please tell me is this right
 

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