A jogger travels a route that has two parts. The first is a displacement A of 2.

Question

A jogger travels a route that has two parts. The first is a displacement A of 2.74 km due south, and the second involves a displacement B that points due east. The resultant displacement A + B has a magnitude of 4.48 km.

(a) What is the magnitude of B, and
(b) what is the direction of A + B as a positive angle relative to due south? Suppose that A - B had a magnitude of 4.48 km.
(c) What then would be the magnitude of B, and
(d) what is the direction of A - B as a positive angle relative to due south?

Explanation / Answer

a)sqrt(2.742+B2)=4.482

B=3.54 km

b)=tan-1(3.54/2.74)=52.3 degrees.

c)sqrt(2.742+B2)=4.482

B=3.54 km

d)=360-tan-1(3.54/2.74)=307.7 degrees.

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