Finding Your Way Home: Vector Components and Trigonometry

In summary, Finn is trying to find his way home from the woods and uses the equations cosine = x + y, sine = y - x. The new vector he calculates is 7cos120 - 0.664 = -4.16.
  • #1
j doe
37
2

Homework Statement


Finn is lost in the woods, trying to find his way back home which he knows is 7.00 km at a 120.0° angle from his current location. He decides to travel 2.00 km at a 40.0° angle followed by another 5.00 km at a 100° angle.

1) What is his current location using a km coordinate plane system and assuming that (0,0) was his starting location?

2) Using information from the previous question, what new vector should Finn plot to get himself home?

Homework Equations

The Attempt at a Solution


1) current location: 2cos40 + 5cos100 = 0.664
2) new vector: 7cos120 - 0.664 = -4.16

can someone please explain to me why you use cosine and those specific numbers together?
 
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  • #2
j doe said:

Homework Statement


Finn is lost in the woods, trying to find his way back home which he knows is 7.00 km at a 120.0° angle from his current location. He decides to travel 2.00 km at a 40.0° angle followed by another 5.00 km at a 100° angle.

1) What is his current location using a km coordinate plane system and assuming that (0,0) was his starting location?

2) Using information from the previous question, what new vector should Finn plot to get himself home?

Homework Equations

The Attempt at a Solution


1) current location: 2cos40 + 5cos100 = 0.664
2) new vector: 7cos120 - 0.664 = -4.16

can someone please explain to me why you use cosine and those specific numbers together?
Have you made a sketch of this problem? That should go a long way to showing you what these distances are.
 
  • #3
Depending on how you measure the angles (clockwise or counter-clockwise, with 0 angle along the x or along the y axis), the cosine is one of the x,y coordinates and the sine is the other. So your calculations are only keeping track of one of the two x,y coordinates. You need similar equations with sine to keep track of the other. Also be careful about which direction is positive and which is negative.
 

What are the components of a vector?

The components of a vector are the horizontal and vertical parts that make up its magnitude and direction.

How do you find the components of a vector?

To find the components of a vector, you can use trigonometric functions such as sine and cosine. The horizontal component is found by multiplying the magnitude of the vector by the cosine of its angle, and the vertical component is found by multiplying the magnitude by the sine of its angle.

What is the difference between magnitude and direction?

Magnitude refers to the size or length of a vector, while direction refers to the angle or orientation of the vector.

Why are components of vectors important?

The components of vectors are important because they allow us to break down a vector into smaller, more manageable parts. This makes it easier to analyze and work with vectors in equations and calculations.

Can you have negative components in a vector?

Yes, components of vectors can be negative. This occurs when the vector is pointing in the opposite direction of the positive axis. For example, a vector with a negative horizontal component would point to the left, while a vector with a negative vertical component would point downwards.

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