# Crow flying to destination (vector problem)

## Homework Statement

A crow flies in two successive displacements to a point that is 80 m to the west. Its first displacement is 80 m in a direction θ1 = 65° west of north.

a)What is the magnitude of its second displacement?

b)What is its direction of its second displacement measured by the angle θ2 measured west from north?

## The Attempt at a Solution

90-65= 25° N of W

cos25°= 80/c --> then c= 80/cos25°= 88.3m

c²=a²+b²

b=√(c²-a²)
b=√((88.3)²-(80)²)
b=37.4m

180°= 25°+90²+Θ
Θx=65°

360°-65°=

295° W of N

## Answers and Replies

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Hello Patrick, and welcome to PF.

In these cases a sketch or a drawing is a big help. I, for instance, can't understand what the c you are calculating, stands for.

I can understand the 25°, though, and I can calculate how much of the 80 m in the westward direction has been covered (call it A). Also how much in the northward direction (call it B). So all I, crow, have to do then is to go west the remainder of the 80 m and south the same distance B. Gives me a magnitude using Pythagoras and an angle via an arctangent.

phinds