How is the displacement and angle of a truck's journey calculated?

[bebe087]

1. A delivery truck travels 10 km north, 18 km east, and 29 km south.

a) What is its final displacement in km from the origin.

b) What is the angle in degree of the final displacement relative to the east.

2. I used the pythagorean theorem to obtain the final displacement from the origin. Then using the displacement found obtained the angle using sign 90 degrees.

3. First I drew an x/y coordinate system. The origin was at 0. Drew a line going 10 km north, 18 km east and 29 km south which puts me 19 km below the origin line.

18^2+19^2=685
The square root of 685 was 26.17 which was the final displacement from the origin.

For the angle, I calculated 26.17sin90 degrees which equaled 26.17. According to the online homework system, both answers were wrong.

What did I do wrong? Please advise. I am completely lost in physics so far.

 

[rl.bhat]

Your calculation of the direction is wrong. You have net x displacement and y displacement. Then tanθ = y/x will give you the direction.

 

[bebe087]

Hi rl.bhat,

Physics is completely foreign to me. Please elaborate. If I use tan(theta)=y/x, what do I plus in for y and x? Also, how can I find final displacement (in km) from the origin?

 

[rl.bhat]

In the given problem x = 18 km and y = - 19 km.