pre calc. question regarding vectors

Question

 

The distance from Parrot Point Airport to the Ivy Cliffs is 270 miles at and angle of 9.4 degrees northeast. There is a wind blowing southeast at 25 miles per hour. You want to make this trip in 3 hours by flying straight there. At what speed* and heading should you fly?

* Round the speed to the nearest tenth of a mile per hour and angle to the nearest tenth of a degree. Where 0≤θ<360 and north is 0 degrees and positive is clockwise.

Answer 1

a southeast wind means from southeast, so the assumption is "a wind blowing southeast at 25 mph"

can be represented by vector magnitude 25 mph and direction 135 degrees counterclockwise from x-axis.

adding wind and plane velocity vectors need to equal destination velocity.

using law of cosine plane velocity=√[90²+25²-2*90*25*cos(54.4),,,,,,,,54.4=(180-80.6)-45

v=78.14mph

the angle made by plane with respect to destination is found with law of sine, call angle b

sin(b)/25=sin(54.5)/78.14

sin(b)=.26,,,,,,,,,, b=15.07 degrees

need to add 15.07 and 9.4 for heading of plane with respect of north, =24.47 degrees

Answer 2

For a simpler solution process, try breaking down the question into x- and y- components. I've attached a video showing you how.