Posted by Matt on Monday, February 18, 2013 at 3:33pm.
A plane is flying 25 degrees north of west at 190 km/h and encounters a wind from 15 degrees north of east at 45 km/h. What is the planes new velocity with respect to the ground in standard position?

Physics  Elena, Monday, February 18, 2013 at 3:54pm
v=190 km/h, α= 25°,
u=45 km/h, β =15°.
V(x) =v•cos α  u•sin β =…
V(y)= v•sinα+u•sinβ=…
V=sqrt{V(x)²+V(y)²}=...
Sine Law:
V/sin(α+ β) =u/sinγ
Solve for γ.
V directed (α+γ)° north of west

Physics  Matt, Monday, February 18, 2013 at 4:15pm
lol can you solve this for me? We have done this multiple times (we think) and we are getting a different answer than that's in the back of the book

Physics  Matt, Monday, February 18, 2013 at 4:26pm
And your answer doesn't match the back of the book either.

Physics  Matt, Monday, February 18, 2013 at 4:26pm
The back of the book says 227 km/h at 162.4 degrees

Physics  Elena, Monday, February 18, 2013 at 4:41pm
V(x) =  v•cos α +u•cosβ =  190cos25 + 45cos15=172.2+43.5= 128.7 km/h
V(y)= v•sinα+u•sinβ= 190sin25 + 45sin15= 80.3 + 11.6 = 91.9 km/h
V=sqrt{V(x)²+V(y)²}= 158.1 km/h
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