Question

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.

Answer 1

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