The two vectors\(\vec{a}\) and \(\vec{b}\) in the figure have equal magnitude of 26 m and the angles are θ1=28° and θ2 = 103°. Find the x-component of their vector sum r.
Find the y-component of their vector sum r.
What is the magnitude of their vector sum r?
Find the angle that their vector sum r makes with the positive direction of the x-axis.
given that : |a| = magnitude of "a" = |b| = magnitude of "b" = 34 m
= (|a| Cos) i + (|a| Sin) j = (34 Cos28) i + (34 Sin28) j = 30.02 i + 15.96 j
= (|b| Cos) i + (|b| Sin) j = (34 Cos(28 + 103) i + (34 Sin(28 + 103)) j = - 22.31 i + 25.66 j
Sum is given as
=+
= (30.02 i + 15.96 j ) + (- 22.31 i + 25.66 j )
= 7.71 i + 41.62 j
hence the x-component of the sum = 7.71 m
the y-component of the sum = 41.62 m
magnitude : || = sqrt((7.71)2 + (41.62)2) = 42.33 m
direction : = tan-1(41.62/7.71) = 79.5 deg counterclockwise from positive x-axis
6, The two vectors and in the figure have equal magnitudes of 34.0 m, and the...
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