The magnitude of a velocity vector is called speed suppose...

The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 60 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 100 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. a) Find the true course b) Find the ground speed of the plane. (Round your answers to one decimal place.)

Transcript

00:01 A boat in running water or an airplane in a blowing wind.

00:06 These are two common examples of what's called relative motion, non -relativistic motion, where the speed and the velocity of the object with respect to the ground comes from adding two vectors.

00:24 So here we're going to take a look specifically at an airplane.

00:28 So the speed is going to be found from the velocity with respect to the ground.

00:38 So i'm writing that as v -sub -g is a vector, velocity with respect to the ground, which is usually what governs how long a flight takes directly anyway.

00:53 The vw is the wind speed and it is a velocity vector.

00:59 Sorry, so that's wind velocity.

01:05 And the bps is the velocity of the plane in still air.

01:16 So pretend that the air were blowing, the wind were blowing.

01:20 And that's usually going to incorporate the heading of the airplane, which direction it snows is pointing as it's trying to fly across the ground.

01:33 So this is very similar to a boat.

01:36 In say a river stream.

01:39 So we're going to take an example of adding those vectors.

01:42 We're going to deal with some compass point directions.

01:47 And the first thing to look at is the wind speed is 60 kilometers per hour.

02:00 And then the direction, let's see how that's written, because that could be a little bit tricky, north, 45 degrees west.

02:12 Okay.

02:14 From north, 45 degrees west.

02:22 So the first thing to be cognizant of when you're dealing with these vectors is the difference between from and two.

02:31 From means the orientation of the tail, whereas two means.

02:42 Okay, so we're going to have to look at the tail.

02:44 The north 45 degree west means start on north and drag your angle 45 degrees to the final western point and i'll show what that means.

03:06 So we'll start with a wind speed and we're going to start on north and we're going to go 45 degrees to the west and we're going to draw the tail.

03:17 So that doesn't look like 45 degrees, by your pardon.

03:22 Not very good at eyeballing angles some days.

03:25 Try to make it go in the middle.

03:28 But we'll show that 45 degrees.

03:32 Just force the issue.

03:34 But what we want to draw there is the tail, not the tip.

03:38 So remember the tip is the other end that has the arrow.

03:44 Duh.

03:45 Okay, never mind.

03:47 So now that is the...

03:49 The wind speed.

03:52 So that is one vector that we're going to have to represent with an x and a y component.