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.
Answers
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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