Draw a vector 𝐬 to represent a wind blowing south at 100 miles per hour for one hour and a vecto

step 1 This question talks about an airplane moving through some wind. We're told that the airplane is

Draw a vector 𝐬 to represent a wind blowing south at 100...

Key Concepts

Vector

A vector is a quantity that has both magnitude and direction. It is commonly represented as an arrow, where the length indicates the size (or magnitude) of the quantity, and the arrow points in the direction of the vector’s effect.

Magnitude

Magnitude describes the size of a vector. It tells you how large a physical quantity is, such as 100 miles per hour for wind or a distance of 300 miles for travel.

Direction

Direction specifies the orientation of a vector in space. In this context, directions like south for wind and east for the plane are used to define the exact route or trajectory of the movement.

Displacement

Displacement is a vector that represents the change in position of an object. It combines both magnitude and direction to describe the overall movement from one point to another, such as a plane traveling a specific distance in a given direction.

Transcript

00:01 This question talks about an airplane moving through some wind.

00:05 We're told that the airplane is moving at 60 degrees east of due north.

00:10 I'm going to draw due north like a dotted line here, and then i'll draw the velocity of this airplane.

00:17 It's 300 miles per hour at 60 degrees east of due north.

00:24 Now remember, a plane's velocity is actually just its velocity relative to the air, not relative to the earth.

00:33 The air, we're told, is actually moving 40 degrees, or excuse me, 30 degrees west of due north at 40 miles per hour.

00:45 So we want to figure out what is the plane's speed relative to the earth if it's moving through the air with the specified velocity and the air is moving with its own specified velocity.

00:57 Well, the way we do this is we simply add these two speeds, to get these two velocities together.

01:05 The velocity of the plane relative to the air plus the velocity of the air relative to the earth will yield the velocity of the plane relative to the earth.

01:14 We're going to use the tip -to -tail method, which is just putting one vector at the end of the next.

01:20 So if i just transfer the wind vector here, we'll have a velocity vector that will look like something like this.

01:31 Now, we're yet lucky because, 30 degrees plus 60 degrees is 90 degrees so the plane and the wind are moving at right angles to each other.

01:43 That means we can use the pythagorean theorem to figure out the magnitude of this velocity.

01:50 I'm going to do that right now...

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