Calculating Tammy's Displacement

[sweet877]

Tammy leaves the office, drives 26 km due north, then turns onto a 2nd highway and continues in a direction of 30.0 degrees north of east for 62 km. What is her total displacement from the office?
The triangle I drew:
|\
|' \ a
|b \
|___\
a = 62 km
b = 26 km
' = 30 degrees

 

[cepheid]

You seem to have her going southeast instead of northeast as it should be.

 

[sweet877]

^ah...right. thanks.

Would Dnet x = 62 cos 30 = 53.7 km
Then Dnet y = 26 km + 62 cos 30 = 57 km
Then total displacement:
sqrt(53.7^2 + 57^2) = 78.3 km?

 

[Tubs]

Yep, that's one way to do it. You could also use the cosine law.

x = [26^2 + 62^2 - 2(26)(62)(cos 120)] ^ .5
x = 78.3