Vector Problem -- Adding up the 3 legs of a hiking journey

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In summary, a vector problem involves finding the magnitude and direction of a quantity in a given situation. To add up the 3 legs of a hiking journey using vectors, you need to break down each leg into its x and y components and then add them together. Vectors make it easier to calculate the total distance and direction of a journey with multiple legs and allow for the application of mathematical principles. While this problem can also be solved using other methods, vectors may provide a more efficient solution. Real-life applications of vector problems include physics, engineering, and navigation.
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NormalForce1
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Homework Statement
A student measures his own walking speed and discovers that it is 1.5 m/s. This student then plans a hike. He plans to start out by walking for 30 minutes due south at his usual constant speed. Then he will turn west slightly so that he is facing 35⁰ west of south, and he will walk (still at the same speed) for 45 minutes in that direction.

After he has completed this first 75 minutes of walking, If the student wants to walk back to where he started from, in what direction should he walk and how long will he need to walk for?
Relevant Equations
a^2 + b^2 = c^2
c^2 = sqrt{a^2+b^2-[2*a*b*cos(theta)]}
I tried finding the resultant vector which was -6360. The magnitude of -6360 is the distance the traveler must travel to reach the start.
I found the angle by using the triangular sum theorem on a right triangle that was split from a scalene triangle. The scalene triangle has side lengths of 6360, 2700, and 3660.
 
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  • #2
:welcome:

Do you have a question?
 
  • #3
Where did you get 3660 from?

I agree with the 2700. Wouldn’t the second leg of the triangle equal 45 x 60 x 1.5?
 

1. What is a vector problem?

A vector problem is a mathematical problem that involves adding or subtracting vectors, which are quantities that have both magnitude and direction. In the context of a hiking journey, vectors can represent the distance and direction of each leg of the journey.

2. How do I solve a vector problem?

To solve a vector problem, you need to break down each vector into its horizontal and vertical components. Then, you can use the Pythagorean theorem and trigonometric functions to find the magnitude and direction of the resultant vector, which represents the total distance and direction of the journey.

3. What is the purpose of adding up the 3 legs of a hiking journey?

Adding up the 3 legs of a hiking journey allows you to determine the total distance and direction of the journey. This information can be useful for planning and navigation purposes, as well as for calculating the average speed or time taken for the journey.

4. Can I use vector addition for any type of journey?

Yes, vector addition can be used for any type of journey, whether it is a hiking trip, a road trip, or a flight. As long as you have the distance and direction of each leg of the journey, you can use vector addition to find the total distance and direction.

5. Are there any limitations to using vector addition for a hiking journey?

One limitation of using vector addition for a hiking journey is that it assumes the journey is taking place on a flat surface. If the journey involves changes in elevation, you may need to use more advanced techniques, such as vector calculus, to accurately calculate the total distance and direction.

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