The two vectors a and b in the figure have equal magnitude of 9 m and the angles are θ1 = 26° and θ2 = 95°. Find the x-component and 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.
from the given data,
ax = a*cos(theta1) = 9*cos(26) = 8.09 m
ay = a*sin(theta1) = 9*sin(26) = 3.94 m
bx = b*cos(theta2) = 9*cos(95) = -0.784 m
by = b*sin(theta2) = 9*sin(95) = 8.97 m
x-component of vector sum, rx = ax + bx
= 8.09 + (-0.784)
= 7.31 m <<<<<<<<<<<<-----------Answer
y-component of vector sum, ry = ay + by
= 3.94 + 8.97
= 12.9 m <<<<<<<<<<<<-----------Answer
the magnitude of their vector sum r, |r| = sqrt(rx^2 + ry^2)
= sqrt(7.31^2 + 12.9^2)
= 14.8 m <<<<<<<<<<<<-----------Answer
angle made by r with +x axis, theta =
tan^-1(ry/rx)
= tan^-1(12.9/7.31)
= 60.5 degrees <<<<<<<<<<<<-----------Answer
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