Exercise 30: Velocities have both direction and magnitude and thus are vectors. The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45◦W at a speed of 40 km/h. (This means that the direction from which the wind blows is 45◦ west of the northerly direction.) A pilot is steering a plane in the direction N60◦E at an airspeed (speed in still air) of 250 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane.

Question

Exercise 30: Velocities have both direction and magnitude and thus are vectors. The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45◦W at a speed of 40 km/h. (This means that the direction from which the wind blows is 45◦ west of the northerly direction.) A pilot is steering a plane in the direction N60◦E at an airspeed (speed in still air) of 250 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane.

I've already gone and completed the problem. Im having trouble converting my degrees that i got for true course (21.55) into the required format (N [value] E)

Answer 1

I suggest you sketch the vectors, and see which way the angle points.

Answer 2

Oh wow, I'm ashamed to say I completely forgot to do that. Thanks! I was able to figure it out, the answer was N68.4E

Thanks!

Answer 3

I agree with your angle.

the angle of 21.55° is expressed in the normal mathematical notation where E is 0° and we rotate counterclockwise, no North is 90° etc.
So look at the NE quadrant, and place your 21.55°
It could technically be noted as E 21.55° N, but the proper notation always says either N or S as the first pointer,
so you want N 68.45° E

notice that 68.45 + 21.55 = 90

Answer 4

To convert the true course angle in degrees to the required format of N[value]E, you will need to follow these steps:

1. Determine the quadrant in which the angle lies. In this case, the true course angle is 21.55 degrees, which falls in the first quadrant (0° to 90°).

2. Determine the direction based on the quadrant:
- First quadrant (0° to 90°): N
- Second quadrant (90° to 180°): S
- Third quadrant (180° to 270°): S
- Fourth quadrant (270° to 360°): N

3. Calculate the value of the angle with respect to the nearest cardinal direction (N, S, E, or W). In this case, the angle is 21.55 degrees, which is closest to N22.45°E.

Therefore, the true course of the plane is N22.45°E.