Solving 2D Vector Problem - Displacement Calculation

[jen333]

Hey, i have a 2D vectors problem here:

A person leaves home, drives 26km due north, then turns onto a second highway and continues in a direction of 30.0 degrees north of east. What is her total displacement?

i've drawn a diagram, and the person's 'path' obviously does not make a right angle triangle. therefore I'm not sure how to calculate displacement for this problem. any hints or pointers greatly appreciated!

-jen

 

[The Bob]

Hey, i have a 2D vectors problem here:

A person leaves home, drives 26km due north, then turns onto a second highway and continues in a direction of 30.0 degrees north of east. What is her total displacement?

i've drawn a diagram, and the person's 'path' obviously does not make a right angle triangle. therefore I'm not sure how to calculate displacement for this problem. any hints or pointers greatly appreciated!

-jen

From what I understand, either you need to know another length (the one of the second highway) or you need to express the displacement in terms of the length of the second highway e.g. you do not have a defined number.

The Bob (2004 ©)

 

[jen333]

oh, sorry! my mistake...
i forgot to add that the person drives for a distance of 62km on the second highway.

-jen

 

[Werg22]

Cosine law...

 

[BobG]

While bross7's method would work, I'm almost sure you're supposed to use the cosine law, as Werg22 said.

A hint: you have side a and you have side b. You also have the angle between them (Angle C).

 

[bross7]

You would be quite right. I got lazy and while technically my method would work, it isn't the best fundamentally.