Question

a vector "a" has magnitude 5.0m and is directed east vector "b" magnitude 4.0m and is directed 35degree west of north. what are the magnitude and the direction of a+b.

Answer 1

Answer:(a) Expressing the vectors in i, j notation, we have:

a = (5.00 m)i

and

b = −(4.00 m) sin 35◦ + (4.00 m) cos 35c

irc

= (−2.29 m)i + (3.28 m)j

So if vector c is the sum of vectors a and b then:

cx = ax + bx = (5.00 m) + (−2.29 m) = 2.71 m

cy = ay + by = (0.00 m) + (3.28 m) = 3.28 m

The magnitude of c is

(2.71 m)2 + (3.28 m)2 = 4.25 m

(b) If the direction of c, as measured counterclockwise from the +x axis is θ then

tan θ =

cy-cx = 3.28 m-2.71 m = 1.211

then the tan−1 operation on a calculator gives

θ = tan^−1(1.211) = 50.4

and since vector c must lie in the first quadrant this angle is correct. We note that this angle

is

90.0 − 50.4 = 39.6

just shy of the +y axis (the “North” direction). So we can also express the direction by

saying it is “39.6 East of North”.

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