Vector addition and displacement

In summary: Since 5.0m points due east, its x-component is also zero. All it is is a y-component.Adding the two x-components together results in a total displacement of 8.0 + 5.0=13.0 meters.
  • #1
MIA6
233
0

Homework Statement


During a rodeo, a clown runs 8.0 m north, turns 55 degrees north of east, and runs 3.5 m. Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is the clown's total displacement?

The Attempt at a Solution


I drew a pic according to the problem, and it looks like a trapezoid, i don't know if it is the right image. How can i find the total displacement's two components? By adding three vectors together? Please explain it to me, thank you.
 
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  • #2
Try using the law of cosines.
 
  • #3
but is this a trapezoid?
 
  • #4
MIA6 said:
but is this a trapezoid?

It might have two sides that are parallel, hard to tell but I don't think that would help you even if it was...
 
  • #5
Try resolving each vector into its horizontal and vertical components, and then add them.
 
  • #6
ok, what's 8.0m's x and y component? its y-component is itslef? the same problem with 5m. hope you can give me some details since i really have no clue.
 
  • #7
MIA6 said:
ok, what's 8.0m's x and y component? its y-component is itslef? the same problem with 5m. hope you can give me some details since i really have no clue.

8.0 meters north means that this displacement has no x component and a y component of + 8.0 meters.

Break into x and y components all three displacement vectors and add all the x and all the y components.
 
  • #8
Well the 8m is directly north, so expressed in terms of its components, it would be <0,8>, so yes, its y component is itself, and its x component is zero. The 5m vector will be <5,0>, since it has no y component.
 
  • #9
You could also turn it into a right triangle and solve with the law of sines only. There are quite a few ways to solve for the total displacement.
 
  • #10
MIA6 said:
ok, what's 8.0m's x and y component? its y-component is itslef? the same problem with 5m. hope you can give me some details since i really have no clue.


Assuming that North is the positive y-axis and East is the positive x-axis:
Since 8.0m points due north, its x-component is zero. All it is is a y-component.
 

What is vector addition?

Vector addition is the process of combining two or more vectors to create a resultant vector. This is done by using the head-to-tail method or the parallelogram method.

What are the rules for vector addition?

The rules for vector addition are as follows: 1) Vectors must have the same units, 2) Vectors can be added in any order, 3) The order of the vectors does not affect the resultant vector, and 4) The resultant vector is the sum of all individual vectors.

How do you find the magnitude and direction of the resultant vector?

To find the magnitude and direction of the resultant vector, you can use trigonometric functions. The magnitude is calculated using the Pythagorean theorem, and the direction can be found using inverse trigonometric functions.

What is displacement?

Displacement is a vector quantity that represents the change in position of an object. It is measured in units of length and has both magnitude and direction.

How is displacement related to vector addition?

Displacement can be calculated using vector addition. By adding all the individual displacements together, you can find the displacement of an object from its initial position to its final position.

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