Solving Motion Problem #2: Angle & Speed Relative to Ground

[shenwei1988]

b) A plane flies at speed 210 km/h in still air. Now, there is a wind blowing at speed 84.3 km/h at 41 degrees to the east of north, and the pilot wishes to fly due north.
1.At what angle should the plane fly? (Assume the angle is measured between the direction of the plane and due north.)
2.With the wind blowing, at what speed does the plane fly relative to the ground?


1. 41? i draw a parallelogram and use the vertical coordinate as the diagonal. is it right?

2. i got completely lost

 

[blochwave]

Three vectors, one is magnitude 210 km/h, it's the direction the plane is pointing except that it's pointing a little westward

another is going due east and is 84.3 km/h

The third vector is the direction the plane should be travelling, due north, at an unknown velocity

If you draw the three vectors you can put them in a right triangle, with two known sides and the unknown angle between them, so you can find the angle with trig

With that right triangle you can also solve for the magnitude of the vector going due north

 

[shenwei1988]

thanks a lot, base on your response. the unknown angle between the two know sides should be 90-41=49 right?

 

[blochwave]

uh-oh, I misread the problem, the wind isn't blowing due east...

It's still similar

draw your axis, you have three vectors. One points an unknown angle to the west, and has magnitude 210km/hr, that's the plane's velocity. One points 41 degrees to the east and is 84.3km/hr, that's the wind

The SUM of those two vectors should be pointing due north. So draw it in a triangle, and one side of the triangle is going north, the wind is coming out 41 degrees to the east, and the plane's velocity connects the two heads.

Now THAT triangle I don't think you can assume is a right triangle, so you may have to use the law of cosines