SOLUTION: An airplane is flying at a velocity of 450 mph due east when it encounters a wind blowing from the southwest at 35 mph. -What is the the planes velocity relative to the ground?

Question 453203: An airplane is flying at a velocity of 450 mph due east when it encounters a wind blowing from the southwest at 35 mph.
-What is the the planes velocity relative to the ground?
- In what direction is it flying as a result of the wind?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Due east is 090 degrees.
From the southwest is a wind from 225 degrees.
-----------
The vector of the plane is 450 to the right.
The wind is magnitude 35 at an angle of 135 degs from the plane's vector.
The plane's ground speed =
=~ 483.89 mph
---------------
Use the Law of Sines to find the angle between 090 and the ground track
483.89/sin(135) = 35/sin(A)
sin(A) = 35*sin(135)/483.89
sin(A) = 0.051145
A = 2.93 degs
Heading = 090 - A = 087.07 degs
= 087 to the nearest degree

RELATED QUESTIONS
a pilot is flying with an airspeed of 185 mph at a heading of 212 degrees. the wind is... (answered by Alan3354)

An airplane is flying at 340 mph with a heading of 210 degrees. If a 50 mph wind is... (answered by Fombitz)

An airplane is flying due east at 340 km/hr. The wind is blowing 40 km/hr at 34 degrees... (answered by Alan3354)

an airplane has a speed of 325 miles per hour in still air. if the plane flies directly... (answered by TimothyLamb,stanbon)

A robin is flying south for the winter at a rate of 40 mph when it runs into a hurricane, (answered by Alan3354)

An airplane can cruise at 255 mph in still air. If a steady wind of 46 mph is blowing... (answered by ikleyn)

An airplane flying at 450 miles/hr due south experiences a westerly wind of 75 miles/hr.... (answered by Fombitz)

An airplane flying due North at 220 kph is blown by a 100 kph strong wind due 50 degrees... (answered by lwsshak3)

an airplane is traveling with a velocity of 320 km/hr to the North. It is flying against... (answered by Alan3354)