(1)A jogger travels a route that has two parts. The first is a displacement vect

Question

(1)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, _______°East 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?________km, ______________° 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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