Question

Consider the two vectors, A and B, for which the length and angle are given below. What would be the x and y components of the the vector sum C = A + B? length of A = 3.606, angle A makes with respect to x-axis = 236.31 degrees length of B = 4.243, angle C makes with respect to x-axis = 45.000 degrees

Cx=

Cy=

Answer 1

C = A + B

for vector R of magnitude r and angle theta

R = r cos(theta)i + r sin(theta)j

c(cos45i + sin45j) = 3.606(cos236.31i + sin236.31j) + (4.243)(cos(theta)i + sin(theta)j)

4.243 cos(theta) = 2 + (cos45)c ...... (i)

4.243 sin(theta) = 3 + (sin45)c ..... (ii)

(i)^2 + (ii)^2 => 4.243^2 ( sin^(theta) + cos^(theta)) = (2^2 + 0.5c^2 + 2.828c) + (9 + 0.5c^2 + 4.243c)

c^2 + 7.0711c - 5 = 0

c = 0.648

Cx = c cos(45) = 0.458  

Cy = c sin(45) = 0.458