Vector Problem: Get Home from 15.0 km Away

[janhen200]

I need help on this vector problem. We haven't started yet, but this was one of the problems on the syllabus.

Your home is 15.0 km at a direction 40 degrees northwest. If you walked 10.0 km north, in what direction and distance would you have to walk to get home?

Your help will be greatly appreciated

 

[pooface]

Welcome to Physicsforums! hope you enjoy your stay.

A vector is a quantity that has a magnitude(like 15 km) and direction (like north or south or an angle such as 40deg).

A good place is always to start with a diagram so you can visually see what is going on.

Your home is 15 km away but 40 degrees north OF west. Can you draw this?

I am not permitted to help you unless you show an effort or ask probing questions.

 

[janhen200]

so far, I've done this and I'm not sure whether or not I am correct.

l \
l \
l \ --->15 km
l \
l___\ ----> 40 degrees

sorry, I am really bad at making diagrams on the computer. It just wanst coming out right. Basically i mae a triangle, with a hypotenuse of 15 and one of the angles (the one opposite the hypotenuse) is 40 degrees.

 

[pooface]

Looks correct to me. However, it is not the angle opposite to the hypotenuse. it is the angle with the x-axis and hypotenuse.

Now you walk north 10km. What direction and distance do you walk to reach home?

 

[janhen200]

Is the answer 11.1?

I used pythagorean theorem.

a=10
b=x
c=15

10^2 + b^2= 15^2

b=11.1
He needs to walk 11.1 km east to get home

Please let me know whether this is right or wrong.

 

[pooface]

yea it is right. Try to keep more decimal places. 11.1 is quite different than 11.18.

 

[janhen200]

Ok, thanks a lot. You've been a great help.