Before starting this problem, review Interactive Solution 1.30. Vector A rightar

Question

Before starting this problem, review Interactive Solution 1.30. Vector A rightarrow has a magnitude of 13.7 units and points due west. Vector B rightarrow points due north. (a) What is the magnitude of B rightarrow if A rightarrow + B rightarrow has a magnitude of 15.3 units? (b) What is the direction of A rightarrow + B rightarrow relative to due west? (c) What is the magnitude of B rightarrow if A rightarrow - B rightarrow has a magnitude of 15.3 units? (d) What is the direction of A rightarrow - B rightarrow relative to due west? Number Units Number Units Number Units Number Units

Explanation / Answer

a)

X = A = -13.7 Units.
Y = B = ?
Z= A+B = 15.3 Units = Resultant.

X^2 + Y^2 = Z^2
(-13.7)^2 + Y^2 = 15.3^2
Y^2 = 15.3^2 - (-13.7)^2 = 234.09 - 187.69 = 46.4
Y = 6.81 Units = B.

b)

Tan Cr = Y/X = 6.81/-13.7 = - 0.497080
Cr = - 26.43 degree = Reference angle.
C = - 26.43 + 180 = 153.57 degree

A-B = A + (-B)
So (c) and (d) can be solved the same way as (a) and (b), but with the direction of B reversed (due south).

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