Question

What is the resultant displacement of the two vectors below? Vector 1: 5.0 cm, W Vector 2: 3.0 cm, S

A. 4.0 cm, 59 degrees West of the South axis
B. 9.7 cm, 31 degrees West of the South axis
C. 8.2 cm, 60 degrees South of the West axis
D. 5.8 cm, 31 degrees South of the West axis

Answer 1

D

Step-by-step explanation:

Answer 2

Answer: D. 5.8 cm, 31 degrees South of the West axis

Step-by-step explanation:

We have two vectors:

Vector 1: (5,0) W

Vector 2: (3,0) S

We need to find the magnitude and direction of the resultant vector:

For the magnitude we will use the formula to calculate the distance
`d` between two points:

`d=\sqrt{{(Y2-Y1)}^(2) +{(X2-X1)}^(2)}` (1)

`d=\sqrt{{(-5 cm - 0 cm)}^(2) +{(-3 cm - 0 cm)}^(2)}` (2)

`d=\sqrt{34 cm^(2)}` (3)

`d=5.83 cm` (4) This is the magnitude of the vector

For the direction, we will use the following formula. Taking into account that if we draw a vector diagram with the resultant vector, we will have a right triangle (whose hypotenuse
`d` was already calculated) and we can use trigonometry in this case:

`sin \theta=(Opposite-side)/(d)` (5)

`sin \theta=(3)/(5.83)` (6)

`\theta= sin^(-1) (3)/(5.83)` (7)

`\theta= 30.96\° \approx 31\°` (8)

Hence, the direction of this resultant vector is
`31\°` South of the West axis.