Vectors for calculus 3?

Question

The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45(degrees)W at a speed of 50 km/h. (This means that the direction from which the wind blows is 45(deg) west of the northerly direction). A pilot is steering a plane in the direction N60(degrees)E at an airspeed of 250 km/h. The true course of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plan is the magnitude of the resultant. Find the true course and ground speed of the plane.

I have no idea what any of that means. Someone please help!!! and explain it!! thank you so much.

Answer 1

this problem requires that you find components of vectors and add them accordingly

the wind is blowing FROM the northwest, so the velocity components of the wind are:

in the + x direction with a speed of 50 cos45=35.3 km/hr

in the -y direction with a speed of 50 sin45=-35.3km/hr

for the plane, the components are:

in the +x direction 250cos30=216.5 km/hr

in the +y direction 250sinsin30=125 km/hr

the components of the plane's speed are then the sums of these components

251.8 in the +x direction

89.7 in the +y direction

magnitude=sqrt[251.8^2+89/7^2]

=267.3 km/hr

direction = arc tan[89.7/251.8]

=19.6 degrees up from the +x axis

Answer 2

When solving this type of problem, you'll need to first analyze each vector forces at play here.

so you need to break down the wind forces into 2 vectors (it's x and y components)  the same thing with the plane.

once you do that, you add the forces (in X and Y directions respectively) of the plane and the wind Separately to get a resultant force vector.

then you use trig to find the resultant force vector (find the hypotnues of the triangle)  

good luck