Solving Vector Problems with Law of Sines and Pythagorean Theorem

[coolkid26]

Homework Statement

So a person walks 10m north, and then walks 18m at a degree of east of south. What is the magnitude and velocity? (Length and angle measure)

Homework Equations

Law of sines
Pythagorean theorem

The Attempt at a Solution

So I split up this problem into two vectors. The first vector is the guy walking north. So his y=8. His x=0 because he doesn't go anywhere in the x direction. Next I created a triangle to figure out the second vector. We know that the angle at the top of the triangle is 30 degrees. The hypotenuse is 18, and at the left bottom side of the triangle is a right angle (connecting the end of the hypotenuse to the y axis. After doing the law of sines the x2 (x of second vector) is 9. y2=15.59. Now I added the x's to get x total (xt) and the y total (yt). xt=9, yt=23.59. Then with these numbers i created a new triangle and did the inverse tan of 23.59 over 9 to get an angle measure of 69.1. Then pythagorean theorem will get me the hypotenuse of this triangle which is 25.25 and the magnitude of the vector. Am i doing this right? I just have a feeling I am not. Thank you for all your help :)

 

[Delphi51]

Something like this?

 

[tomcue]

I would say that your approach seems to be correct. You have used the Law of Sines and Pythagorean Theorem to solve for the magnitude and direction of the second vector. However, I would recommend double checking your calculations and using units (meters) throughout the problem to ensure accuracy. Additionally, it may be helpful to draw a diagram to visualize the problem and your solutions. Overall, it seems like you have a good understanding of vector problems and how to solve them using these mathematical principles. Keep up the good work!