Question

Pre-Cal Help!!! (See Attachment)

Answer 1

In order to arrange the given vectors (u, v, w, x, y, and z) in ascending order of the magnitudes of their vector sums with vector t, you have to follow this procedure:

1) find the coordinates of vector t

2) find the coordinates of the other given vector (u, v, w, x, y, or z)

3) add the corresponding coordinates

4) find the magnitude of the sum vector using the formula

Let's do it:

1) vector t

x-coordinate = 4m/s * cos(60°) = 2 m/s
y-coordinate = 4m/s * sin(60°) = 3.46 m/s

2) u+t

vector u: 3m/s, angle 120°=> second quadrant

x-coordinate = - 3 m/s * cos(60°) = -1.5 m/s
y-coordinate = 3m/s * sin(60°) = 2.6 m/s

u + t:
x-coordinate = 2 - 1.5 = 0.5
y-coordinate = 3.46 + 2.6  = 6.06

$magnitude = \sqrt{(0.5)^2+(6.06)^2} =6.08$

3) v + t

vector v: 4.5 m/s , angle 135°

x-coordinate = - 4.5 * cos(180°-135°) = -4.5 * cos(45°) = -3.18
y-coordinate = 4.5 * sin (180° - 135°) = 4.5 * sin(45°) = 3.18

v + t
x-coordinate = 2 - 3.18 = - 1.18
y-coordinate = 3.46 + 3.18 = 6.64

$magnitude= \sqrt{(-1.18)^2+(6.64)^2}= 6.74$

4) w + t

vector w: 4m/s, angle 45°

x-coordinate = 4 * cos(45°) = 2.83
y-coordinate = 4 * sin(45°) = 2.83

vector w + t
x-coordinate = 2+2.83 = 4.83
y-coordinate = 3.46+2.83 = 6.29

$magnitude= \sqrt{ (4.83)^{2} + (6.29)^{2} } =7.93$

5) x + t

vector x: 6 m/s, angle 210°C => third quadrant

x-coordinate = - 6 * cos(30°) = - 5.2
y-coordinate = - 6 * sin(30°) = - 3

x+t
x-coordinate = 2 - 5.2 = - 3.2
y-coordinate = 3.16 - 3  = - 0.16

$magnitude= \sqrt{ (-3.2)^{2} + (-0.16)^{2} } =3.20$

6) y+t

vector y: 5m/s, angle 330°=> fourth quadrant

x-coordinate = 5 *cos(360° - 330°) = 4.33
y-coordinate = - 5 * sin(30°) = -2.5

vector y+t
x-coordinate = 4.33 + 2 = 6.33
y-coordinate = - 2.5 + 3.46 = 0.96

$magnitude= \sqrt{ 6.33^{2} + 0.96^{2} } =6.40$

7) z+t

vector z = 7m/s angle 240° => third quadrant

x-coordinate = - 7 * cos(60°) = - 3.5
y-coordinate = - 7 * sin(60°) = - 6.06

vector z + t
x-coordinate = 2 - 3.5 = - 1.5
y-coordinate = 3.46 - 6.06 = -2.6

magnitude = 3.00

Now, you have all the numbers and just have to order them.