Answer:
Option a: magnitude = 1.6 cm and angle = 40.3°
Explanation:
This problem consists of a sum of vectors
To make this sum, we need to decompose each vector in x and y components, using their angles.
So, for vector u, we have:
u_x = u*cos(340) = 3 * 0.9397 = 2.8191
u_y = u*sin(340) = 3 * (-0.342) = -1.026
Now for vector r we have:
r_x = r*cos(128) = 2.6 * (-0.6157) = -1.6008
r_y = r*sin(128) = 2.6 * 0.788 = 2.0488
Now we need to sum the x components and the y components to find the resultant of r + u. Let's call the resultant vector k:
k_x = u_x + r_x = 2.8191 - 1.6008 = 1.2183
k_y = u_y + r_y = -1.026 + 2.0488 = 1.0228
To find the magnitude and the angle, we can use Pythagoras's formula and arc tangent of k_y/k_x:
magnitude = sqrt(1.2183^2 + 1.0228^2) = 1.5907 cm
angle = arc tangent(1.0228/1.2183) = 40.0145°
So the nearest answer is option a: magnitude = 1.6 cm and angle = 40.3°