Question

A car travels 87 miles north and

then 114 miles west.
What is the direction of the car's
resultant vector?
Hint: Draw a vector diagram.
0 = [?]
Round your answer to the nearest hundredth.
Enter

Answer 1

The resultant vector (also known as the displacement vector) can be found by drawing a triangle connecting the starting point, the end point, and the origin, where the starting point is (0, 0) and the end point is (87 miles, 114 miles).

Using trigonometry, we can find the resultant vector's component values as follows:

Let x be the horizontal Component and y be the vertical Component

87 miles = 114 miles * sin(θ)

y = 87 miles * cos(θ)

To find θ, we can use the inverse trigonometric function arc sinus of y/x:

θ = arcsin(87/114)

Arcsin(87/114) ≈ 35.3°

So the direction of the resultant vector is approximately 35.3° counterclockwise from the positive x-axis

Round the answer to the nearest hundredth: 35°14'

So the direction of the resultant vector is approximately 35°14' counterclockwise from the positive x-axis

Answer 2

The direction of the car's resultant vector is approximately 38.27 degrees west of north.

To find the direction of the car's resultant vector, we can use trigonometry. We have the distances the car travels north and west, and we can treat them as the legs of a right triangle. The resultant vector represents the hypotenuse of this right triangle.

Let's use the following notation:

- Distance traveled north (opposite side) = 87 miles

- Distance traveled west (adjacent side) = 114 miles

- θ (theta) = the angle between the resultant vector and the north direction

We can use the tangent function to find θ:

tan(θ) = (opposite side) / (adjacent side)

tan(θ) = 87 / 114

Now, calculate θ:

θ = arctan(87 / 114)

Using a calculator to find the arctan (inverse tangent) of 87/114, we get:

θ ≈ 38.27 degrees

So, the direction of the car's resultant vector is approximately 38.27 degrees west of north.