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Relative to the ground, a car has a velocity of 16.0 m/s, directed due north. Relative to this car, a truck has a velocity of 24.0 m/s, directed 52.0 north of east. What is the magnitude of the truck’s velocity relative to the ground?

$v_{T G}=37.91 \mathrm{m} \cdot \mathrm{s}^{-1}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

03:03

Relative to the ground, a …

03:07

05:49

Go Relative to the ground…

02:52

04:31

Two vehicles approach an i…

02:41

A $1500 \mathrm{~kg}$ car …

03:15

A car is driving directly …

01:45

An airplane has a velocity…

01:03

A car is traveling west at…

01:10

01:23

A $2000-\mathrm{kg}$ truck…

01:09

A truck travels $3.02 \mat…

04:04

A bicyclist rides at $8.00…

01:11

A car is traveling east at…

You are in a hot-air ballo…

02:16

Suppose a boat moves at 12…

02:22

So the question is this that a car moving at 16 meters per second due north sees a truck moving at 52 degrees north of east at 24 meters per second. And we're trying to find what the magnitude of the, uh trucks velocity is relative to the road. So to do this, we need to first draw some vectors on here. So the vector that describes the, um car relative to the roads were saying, This is going to be the origin, Um, and it's relative to the road. So vector that describes the car relative to the road is this vector points straight north, and it's 16 meters per second. And the victor that's going to describe the, um, truck relative to the car. So this point is a relative to the car, and it's 52 degrees above the horizontal. Well, look something like this. So this is a 52 degree angle and the truck is moving at 24 meters per second. So if we want to find the speed of the truck relative to the road, we need to find the vector shown that connects the origin to this point here. So to find this. Ah, vector. Here we need to first write the two vectors that we know already in vector form. This will make it a little bit easier. So the vector that describes the car relative to the road is just zero 16. We're saying that North South is R Y. Direction in East West is our X direction On and up is positive and to the right is positive. And for the, um, truck that the velocity of the truck relative to the car we can write the vector of the velocity as 24 co sign of 52 degrees and 24 sign of 52 degrees. And we know this because sign of 52 degrees is opposite over I bought news. And opposite in this case is the vertical component of the frosty. And same thing goes for the, uh, horizontal component of lost E. It's co signer 15 52 degrees is adjacent over iPod news where Jason is the, um, horizontal component of lost e. So we can just sell for those. So now that we know these two, we can Adam together, and that will give us this vector here which will call capital of the that connects the origin and the tip of this vector. Um, that's moving at 24 meters per second. So adding them together we get 24 co sign 52 degrees and 16 plus 24 times sign of 52 degrees. And to take the magnitude of this vector, we know that the magnitude is equal to the horizontal component squared, plus the vertical component squared. And so we can plug each of these in and calculate V, which ends up being 37 0.91 meters per second, and that's all right.

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