172k views
4 votes
Given a vector with a placement of 810 m and a positive direction of 18 degrees above the x-axis, what are the x and y components of the vector?

User Lonix
by
8.1k points

1 Answer

3 votes

Final answer:

The x and y components of a vector with a magnitude of 810 m and directed 18 degrees above the x-axis are found using cosine and sine functions, yielding approximately 770.39 m for the x-component and 250.29 m for the y-component.

Step-by-step explanation:

To find the x and y components of a vector with a magnitude of 810 m and a direction of 18 degrees above the x-axis, you can use trigonometry. The x-component (horizontal) can be found using the cosine function, and the y-component (vertical) using the sine function.

The formulas are as follows:

  • x-component = magnitude × cos(direction)
  • y-component = magnitude × sin(direction)

For a vector with a magnitude of 810 m and a placement of 18 degrees above the x-axis:

  • x-component = 810 m × cos(18°)
  • y-component = 810 m × sin(18°)

Plugging in the values:

  • x-component = 810 m × 0.9511 (cos(18°)) ≈ 770.39 m
  • y-component = 810 m × 0.3090 (sin(18°)) ≈ 250.29 m

Therefore, the vector's x-component is approximately 770.39 m, and the y-component is approximately 250.29 m.

User Aqsa Arshad
by
8.7k points