Question

Find the y-component of this vector: 22.3 m 77.1° Remember, angles are measured from the +x axis.​

Answer 1

-21.7m

Step-by-step explanation:

To find the y-component of the vector, we need to find the vertical displacement from the point at the bottom of the vector to the x-axis (or its y-coordinate value).

To calculate this we can create a triangle with the vector as the hypotenuse, the y-axis as the second side and draw an imaginary line from the end of the vector directly horizontally across to the y-axis.

We can use the given angle to find the angle between the y-axis and the angle. Since the angle of a quadrant is 90 degrees, the angle within our triangle must be
`90-77.1=12.9` degrees.

From here, to find the length of the side on the y-axis we can use the trigonometric cos function.

`cos \theta =(adjacent side)/(hypotenuse)`

Therefore
`cos 12.9=(y-component)/(22.3)` and
`ycomponent = 22.3cos12.9`

This gives us a value of 21.7 (3.s.f) for our y-component.

Finally, the y-component is also a vector so it also needs a direction. Therefore like its coordinate, its value will be -21.7m.