A point (x, y) can be written in polar form as (R, θ), such that:
x = R*cos(θ)
y = R*sin(θ)
Where R is the magnitude and θ is the angle measured from the positive x-axis that defines the direction.
The correct answers are:
a) You can see the image at the end.
b) A = (2.82m, -1.03m)
B = (0m, 2.0m)
C = (-4.7m, -1.7m)
c) D = (2.02m, 21.22°).
a) Let's define east as the positive x-axis, north as the positive y-axis.
Here we have:
A = (3.0m, 20° sout of east) = (3.0m, -20°)
B = (2.0m, north) = (2.0m, 90°)
C = (5.0m, 70° sout of west) = (5.0m, 250°)
The graph of the 3 vectors can be seen in the image below.
b) We want to write A, B, and C in component form.
We start with A = (3.0m, -20°)
x = 3.0m*cos(-20°) = 2.82m
y = 3.0m*sin(-20°) = -1.03m
A = (2.82m, -1.03m)
B = (2.0m, 90°)
x = 2.0m*cos(90°) = 0m
y = 2.0m*sin(90°) = 2.0m
B = (0m, 2.0m)
C = (5.0m, 250°)
x = 5.0m*cos(250°) = -1.7m
y = 5.0m*sin(250°) = -4.7m
C = (-4.7m, -1.7m)
c) Now we want to find the magnitude and direction of:
D = A + B + C
= (2.82m, -1.03m) + (0m, 2.0m) + (-4.7m, -1.7m)
= (2.82m + 0m - 4.7m, -1.03m + 2.0m - 1.7m)
= (-1.88m, -0.73m)
The magnitude is given by:
[tex]R = \sqrt{(-1.88)^2 + (-0.73)^2} = 2.02m[/tex]
To find the direction, or the angle, we can write:
θ = Atan(y/x) = Atan(-0.73m/-1.88m) = 21.22°
Then we can write D as:
D = (2.02m, 21.22°).
If you want to learn more, you can read:
https://brainly.com/question/12053471
