Homework Help: physics

Posted by Amanda on Monday, September 3, 2012 at 7:11pm.

Tammy leaves the oﬃce, drives 43 km due
north, then turns onto a second highway and continues in a direction of 30◦
north of east for 80 km.
What is her total displacement from the office?
and
At what angle is her displacement? (Consider east to be 0◦ and north 90◦.)
please help! I got 40 and 24.8 and they are both wrong ;(

physics - Elena, Tuesday, September 4, 2012 at 11:30am
the angle that the second part makes with the first part of the path is 90+30=120º.
Using cosine law,
displacement = sqrt(43² +80²-2•43•80•cos120º) =108 km.
From the sine law
108/sin120 = 80/sinα
sinα=80•sin120/108= 0.64
α =39.9º (the angle which displacement makes with north direction)

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