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

Question

A jogger travels a route that has two parts. The first is a displacement vector A of 3.40 km due south, and the second involves a displacement vector B that points due east.
(a) The resultant displacement vector A + vector B has a magnitude of 5.46 km. What is the magnitude of vector B ?_______km
What is the direction of vector A + vector B relative to due south?_____°(east of south or west of south?)

(b) Suppose that vector A - vector B had a magnitude of 5.46 km. What then would be the magnitude of vector B and what is the direction of vector A - vector B relative to due south?
magnitude of vector B : ____________km
direction of vector A - vector B relative to due south :_______°(east of south or west of south?)

Explanation / Answer

a) vector A = (0i - 3.4j)
vector b = (xi + 0j)

vector sum = (0i - 3.4j) + (xi + 0j) = (xi - 3.4j)

magnitude of vector sum = 5.46 km

(-3.4)2 + x2 = 5.462

x2 = 18.2516

x = 4.27 km

since the i-componet is positive and j-component is negative, the direction is south east.

direction: tan-1 (3.4/4.27) = 38.5 degree east of south.

b) vector A = (0i - 3.4j)

vector b = (xi + 0j)

vector sum = (0i - 3.4j) - (xi + 0j) = (-xi - 3.4j)

magnitude of vector sum = 5.46 km

(-3.4)2 + (-x)2 = 5.462

x2 = 18.2516

x = 4.27 km

since the i-componet is negtive and j-component is negative, the direction is south east.

direction: tan-1 (3.4/4.27) = 38.5 degree west of south.

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