Question

Find the x- and y-components of the vector d⃗ = (9.0 km , 26 ∘ left of +y-axis). Express your answer in kilometers. Enter the x and y components of the vector separated by a comma.

Answer 1

To find the components of the vector d⟵ = (9.0 km, 26° left of +y-axis), we calculate the x-component as -3.964 km and the y-component as 8.049 km, using the trigonometric functions sine and cosine with respect to the given angle.

Step-by-step explanation:

The student is asked to find the x- and y-components of a vector d⟵ = (9.0 km, 26 ° left of +y-axis). To find the components, we can use trigonometric functions since the vector makes an angle with the axes. The x-component (dx) can be found using the cosine function and the y-component (dy) using the sine function because the vector is angled in relation to the y-axis. As the angle given is 'left of the +y-axis', it means that we are dealing with a counter-clockwise rotation from the positive y-axis.

Therefore, for a vector d making a 26° angle with the y-axis, the components are calculated as:

dx = d * sin(26°) = 9.0 km * sin(26°) = 3.964 km (rounded to three decimal places)

dy = d * cos(26°) = 9.0 km * cos(26°) = 8.049 km (rounded to three decimal places)

Note that the x-component will be negative since it is to the left of the y-axis, and by convention, leftward is negative on the x-axis.

Thus, the x- and y-components of the vector d⟵ are -3.964 km, 8.049 km, respectively.

Answer 2

(-8.089 km, 3.945 km)

Step-by-step explanation:

We need to find the x- and y-components of the following vector :

d (9 km, 26 degrees left of +y axis)

We know that the x and y component of any vector is given by :

`d_x=d\ cos\theta`

`d_y=d\ sin\theta`

So, x component :

`d_x=-9* cos(26)=-8.089\ km`

y component :

`d_y=9* sin(26)=3.945\ km`

So, the x and y components of the vector separated by a comma are (-8.089 km, 3.945 km). Hence, this is the required solution.