Question

Vector V₁ is 6.8 units long and points along the negative x-axis. Vector V₂ is 8.2 units long and points at 55° to the positive x-axis.

What are the x and y components of vector V₁?
What are the x and y components of vector V₂?
Determine the magnitude of the sum V₁+V₂.

Answer 1

The x component of V₁ is -6.8 and the y component is 0. The x component of V₂ is approximately 4.67 and the y component is approximately 6.56. The magnitude of the sum V₁+V₂ is approximately 6.90 units.

Step-by-step explanation:

To find the x and y components of vector V₁, we need to consider that it points along the negative x-axis. Since it points in the negative x direction, the x component of V₁ is -6.8 and the y component is 0.

For vector V₂, we need to use the given angle of 55 degrees to find the x and y components. The x component can be found using the formula x = magnitude * cos(angle), so x = 8.2 * cos(55) ≈ 4.67. The y component can be found using the formula y = magnitude * sin(angle), so y = 8.2 * sin(55) ≈ 6.56.

To find the magnitude of the sum V₁+V₂, we can add the x components and the y components separately. The x component of the sum is -6.8 + 4.67 = -2.13. The y component of the sum is 0 + 6.56 = 6.56. We can then use the Pythagorean theorem to find the magnitude R of the sum: R = sqrt((-2.13)^2 + 6.56^2) ≈ 6.90 units.