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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 37^{o} South of West. What is the required heading pf the plane?
2. Relevant equations
V_{PE} = V_{PW} + V_{WE}
3. The attempt at a solution
Horizontal component
V_{PE} = V_{PW} + V_{WE}
0 = xcosᵝ  80cos37
xcosᵝ = 80 cos37 (1)
Vertical component
V_{PE} = V_{PW} + V_{WE}
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
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 37^{o} South of West. What is the required heading pf the plane?
2. Relevant equations
V_{PE} = V_{PW} + V_{WE}
3. The attempt at a solution
Horizontal component
V_{PE} = V_{PW} + V_{WE}
0 = xcosᵝ  80cos37
xcosᵝ = 80 cos37 (1)
Vertical component
V_{PE} = V_{PW} + V_{WE}
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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