a) (2 points) Express the plane’s direction and speed as a vector. Give your answer in ai+ bjform.

Question

A plane’s bearing is S 33o E and is going 600mph. A 75 mph headwind is blowing in the direction N 76o W.Assume that the pilot has not taken the wind into account and has not corrected the course. The position vectors given below might be helpful. Vectoradenotes the airplane and vector W denotes the wind. Round all answers to 2 decimal places.

Answer 1

S33E at 600

N76W at 75

180-76+90-33=

161 degree angle between them

construct a parallelogram with sides 600 and 75,

then find the diagonal's length= resultant vector's magnitude. then find it's vertical and horizontal components, which = V + W

or calculate V and W, and add them

V=<600cos33, -600sin33>

W = <-75cos76, 75sin76>

V+W=<a,b>=<600cos33-75cos76, -600sin33+75sin76>

ai+bj

=(600cos33-75cos76)i + (-600cos33+75sin76)j

or use an online vector addition calculator