Calculating Distance and Displacement in Vector Problems

[barroncutter]

Homework Statement

Darryl drives his load of tomatoes 14.0 km [E], 6.0 km [N], 12.0 km [N 15° E], and
then 2.0 km [N 65° E]. This takes him 42 minutes. Calculate Darryl’s distance
and
displacement. Then draw a diagram to show your work.
[/B]

Homework Equations

Not really sure.[/B]

The Attempt at a Solution

I'm honestly really confused... not really sure where to go from here. [/B]

 

[TomHart]

Welcome to Physics Forums.

The way you graphically add vectors is to start by drawing one vector. Then you draw the second vector such that its starting point is at the previous vector's endpoint. You then continue doing that until all of the vectors have been drawn. Then to find the sum of all of the vectors, you draw a vector from the starting point of the first vector to the end point of the last vector. It is basically what you have done in your diagram, except you should draw arrows at the endpoints of the vectors. So you should have an arrow at the right end of d1, the upper end of d2, the upper end of d3, and the upper end of d4. And your vector that represents the sum of those vectors would start at the starting point of d1 and end at the end point of d4 with an arrow at d4. You have a dashed line connecting those points, but you should make it a solid line with an arrow at the end at d4 to indicate the direction of the resultant vector. The magnitude and direction of the resultant vector will be the displacement.

To add them mathematically, the most straightforward way is to break every vector down into its x and y components. Next, sum all of the x components and sum all of the y components. From the resultant x and y vectors, you can find the magnitude and direction of the final resultant vector.

 

[CWatters]

+1

What scale is your drawing?

Darryl drives his load of tomatoes 14.0 km [E]

Your drawing appears to represent that with line d1 but it's 22 squares long not 14 as I would expect.

6.0 km [N]

Your drawing appears to represent that with line d2 but it's 9.5 squares long.

 

[CWatters]

The question says to calculate the distance and displacement and then do the drawing but I would do the scale drawing first and use that to help work out what calculations are required as per TomHarts comment.