Vector Problem Homework: Finding Cyclist B's Route to Campground

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In summary, the two cyclists, A and B, started off traveling to a campground. Cyclist A traveled due east for 1240m, then turned north and traveled for 1600m, ending at the campground. Cyclist B started off going north for 1960m, then stopped and asked for directions. The vector that will take cyclist B to the campground is 1291 m at an angle of 16.19° south of east.
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theintarnets
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Homework Statement


Two cyclists, A and B, start off traveling to a campground. Cyclist A travels due east for 1240m, then turns north and travels for 1600m, ending at the campground.
Cyclist B starts off going north for 1960m, then stops, confused and lost, and asks for directions. Calculate the vector that will take cyclist B to the campground, specifying both magnitude and direction.


Homework Equations





The Attempt at a Solution


I've attached an image of my attempt. I'm not sure if it's correct or not. If someone could take a look at it and point me in the right direction, I'd really appreciate it! My final answer is that the cyclist must travel 16.19° South of East for 1291 m, but I really want to make sure my process is correct.
 

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  • #2
theintarnets said:

Homework Statement


Two cyclists, A and B, start off traveling to a campground. Cyclist A travels due east for 1240m, then turns north and travels for 1600m, ending at the campground.
Cyclist B starts off going north for 1960m, then stops, confused and lost, and asks for directions. Calculate the vector that will take cyclist B to the campground, specifying both magnitude and direction.

Homework Equations



The Attempt at a Solution


I've attached an image of my attempt. I'm not sure if it's correct or not. If someone could take a look at it and point me in the right direction, I'd really appreciate it! My final answer is that the cyclist must travel 16.19° South of East for 1291 m, but I really want to make sure my process is correct.
That looks fine to me !
 

FAQ: Vector Problem Homework: Finding Cyclist B's Route to Campground

What is a vector and why is it important in science?

A vector is a mathematical quantity that has both magnitude and direction. It is important in science because it is used to represent physical quantities such as velocity, acceleration, and force, which are essential in understanding the behavior of objects in the natural world.

How do I solve a vector problem?

To solve a vector problem, you first need to identify the given vectors and their direction and magnitude. Then, use vector addition or subtraction to find the resultant vector. Finally, use trigonometric functions to break down the resultant vector into its horizontal and vertical components.

Can vectors be added or subtracted?

Yes, vectors can be added or subtracted using the parallelogram or triangle method. This allows us to find the resultant vector, which is the combination of two or more vectors.

What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include speed and temperature, while examples of vectors include velocity and displacement.

How are vectors used in real-world applications?

Vectors are used in many real-world applications, such as navigation systems, engineering, and sports. They are also essential in understanding and predicting the motion of objects, such as projectiles and planets. Additionally, vectors are used in computer graphics to represent images and animations.

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