Question

The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 140, bearing 160°
v: magnitude 200, bearing 290°
w: u + v

A. w: (282, 141°)
B. w: (23603, 226°)
C. w: (153.6, 246°)
D. w: (22, 182°)

Answer 1

@satellite73 Can you help?

Answer 2

u: magnitude 140, bearing 160°
v: magnitude 200, bearing 290°
find u + v
First convert polar (r,θ) to rectangular (x,y)
x = r cos(θ)
y = r sin(θ)
u: x = 140 cos 160° and y = 140 sin 160°
x = -131.557 and y = 47.883
v: x = 200 cos 290° and y = 200 sin 290°
x = 68.404 and y = -187.939
add x and y components
x = -131.557 + 68.404 = -63.153
y = 47.883 + -187.939 = -140.056

convert rectangular coordinates back to polar coordinates
r = √-63.153² + -140.056²
r = 153.6
θ = 270 - arctan(63.153/140.056)
θ = 245.73
w: (153.6, 245.73°)

Answer 3

I can try, but i have to warn you im not that good at these