Solving the Dog's Displacement: Vectors & Magnitude

In summary, a lost dog traveled 30 degrees south of west for 450m and then ran at 20 degrees east of north for 600m. Using vector components and calculating the magnitude, the dog's displacement is approximately 385.8m. It is possible to use either angle 20 or 70, but cos20 and sin70 must be used for the vertical component.
  • #1
nadong2dong
15
0

Homework Statement


A lost dog travels 30 degrees south of west for 450m. He then smells some food and sprints at 20 degrees east of north for 600m.


Homework Equations


a) Draw each vector. Label the magnitude and thetas.
b)Calculate the vector components
c) calculate the magnitude of the dog's displacement.



The Attempt at a Solution


a) I am confused with the second part of the question. Should i use the angle "20degrees" as the theta? or 70 ?
b) first part
-450cos30 = -389.7
-450sin30 = -225
second part ( confused with this part, i used 70 degrees, instead of 20)
600cos70 = 205.2
600sin70= 563.816
c) -389.7+ 205.2 = -184.5 <<<<< X component
-225 + 563.8 = 338.816 <<<<<<< Y component

Square root[ (-184.5)^2 + (338.816)^2 ] = 385.8 m <<< the magnitude of the dogs displacement.
 
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  • #2
You can use either angle 20 or angle 70. Then you have to use cos20 for the vertical component BUT sin70 for the same component.
 

FAQ: Solving the Dog's Displacement: Vectors & Magnitude

What is displacement in the context of a dog's movements?

Displacement refers to the overall change in position of a dog, taking into account both distance and direction. It is a vector quantity, meaning it has both magnitude (numerical value) and direction.

How do you calculate displacement using vectors?

To calculate displacement, you can use the Pythagorean theorem to find the magnitude of the vector and use trigonometry to determine the direction. Alternatively, you can use a graph to plot the starting and ending locations of the dog and measure the distance and direction between them.

Why is displacement important to understand in relation to a dog's movements?

Displacement is important because it provides a more comprehensive understanding of a dog's movements, as it takes into account both distance and direction. This is especially useful for tracking a dog's location and analyzing its behavior.

How does magnitude relate to displacement in the context of a dog's movements?

Magnitude is a crucial component of displacement, as it represents the numerical value of the overall change in position. In the context of a dog's movements, it can help determine the distance traveled or the speed at which the dog is moving.

Can displacement be negative in the context of a dog's movements?

Yes, displacement can be negative in the context of a dog's movements. This occurs when the dog moves in the opposite direction of its initial position, resulting in a negative value for the displacement vector. For example, if a dog starts at point A and ends at point B, but moves in the opposite direction from point B back to point A, the displacement would be negative.

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