How Do You Calculate Displacement in a Multi-Directional Jogging Route?

[micahps]

1. A jogger runs directly east for 4 km, then turns and goes northwest for 9 km. He then travels directly south for 5 km. How far is he from the starting point? (km) In what direction is he from the starting point(measured as an angle counterwise from the east axis, units are deg)? (Northwest is the direction lying exactly half way between north and west.)


2. magnitude of displacement= A+B+C



3. I've drawn out the vectors. I'm thinking that I should find the x and y componets of each vector, add the componets, and add the square of the x and y and take the square root. I'm just unsure about how to go about doing this!

 

[dulrich]

You've outlined the method correctly in #3.

As you said, the first step is to calculate the components of each vector. What is the formula for this?

You will need to take into account the direction of each displacement. What are the relevant angles?

 

[bharath423]

i think there is no need of vector analysis for this,we are just dealing with distance and angles so mathematical funda would be enough,maybe the diagram i have attached may show what i say...

 

[dulrich]

Vectors are the mathematics of distances and angles. You are doing vector math right now! You mentioned vectors (and magnitude, components) so I figured you knew that.

Your diagram looks right.

Think about the 9 km northwest leg and break it down into north vs. west. In this leg how far north does the jogger go? How far west?

The 9 km on your diagram is the hypoteneus of a right triangle (one of the other angles is the 45 degree you have labeled on the right). You'll need some trig to get the answers you need.

 

[bharath423]

thank you dulrich,yup that's all it needed..may micahps too understand it...

 

[micahps]

Thank you all for replies! I got the solution by following the steps I outlined in 3. It wasn't hard after I broke everything down.