Math problem?
1) The manitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 140, bearing 160 degree
v:magnitude 200, bearing 290 degree
w: u + v
a) w: (282, 141.4degree)
b) w: ( 153.6, 226 degree)
c) w: ( 23603, 226 degree)
d) w: (22, 182.1 degree)
Thanks
Comments
None of the above.
First draw a picture of x and y axes. This will allow an understanding of the resultant, keep the signs correct, and keep all the angles used between 0 and 90.
u points left, 20 degrees above the negative part of the x-axis.
v points sharply down to the right, 20 deg to the right of the negative y axis
So we will only use the sin and cosine of 20 deg and use the picture to get + and - signs.
We break each vector into its components along the x and y axes.
xu= -140 cos(20)=-131.56
yu= +140 sin(20)=+47.88
xv= +200 sin(20) = +68.40
yv = -200 cos(20) = -187.93
then xw= xu+xv = -63.16
yw = yu + yv = -140.05
The w vector, having both x and y negative, points down to the left. Length is sqrt(xw*xw + yw*yw)= 153.63
and angle to the left of straight down (270) is
arctan(xw/yw)=24.27 deg
So the final angle of w is 270-24.27=245.73 deg
w: (153.6, 245.7)