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

Question

A plane’s bearing is S 33oE and is going 600mph. A 75 mph headwind is blowing in the direction N 76oW. 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. Vector a denotes the airplane and vector w denotes the wind. Roundall answers to 2 decimal places.

Answer 1

This question adds a little but more information than is necessary, so the first thing we must do is pick out the necessary information. Since we are concerned with the headwind, we'll look just at the speed and direction of the headwind.

First, we look at the headwind's direction, 76° north of west. When we obtain directions like these, it's important that start at the second cardinal direction mentioned (in this case, west) and move toward the first cardinal direction (in this case, north). In terms of a coordinate plane, the headwind is making an angle of 76° with the negative x-axis and our vector will be in the second quadrant, meaning the x-component will be negative and the y-component will be positive.

Now that we have those preliminaries out of the way, we can get into the equations! The components of the headwind will be

W_x= -75cos(76°)

W_y= 75sin(76°)

Where we use cosine to find the x-component because that the the axis that the angle is being made with. Plugging this into our calculators, we get a final answer of

W= -18.14i+72.77j