Question

A vector makes an angle,��, with the horizontal. The horizontal and vertical components of the vector will be equal in magnitude if angle�� is?

1) 30 degrees
2) 45 degrees
3) 60 degrees
4) 90 degrees

Answer 1

The horizontal and vertical components of a vector are equal in magnitude when the vector makes a 45-degree angle with the horizontal.

Step-by-step explanation:

The horizontal and vertical components of a vector will be equal in magnitude if the angle θ the vector makes with the horizontal is 45 degrees. This is because the cosine and sine of 45 degrees are equal, which leads to equal magnitude when these functions are applied to decompose the vector into its horizontal and vertical components.

For a vector with an angle of 30 degrees to the horizontal, we can calculate the magnitude of the vector given its x-component (horizontal component) using the relationship Ax = A cos θ. Since Ax is given here as 3 units, and cos(30) is
`√3/2`, the magnitude of the vector A is A = Ax / cos(30) which equals
`3 / (√3/2)` = 3.46 units (approx.).

Therefore, the correct angle for equal magnitude of the horizontal and vertical components is 45 degrees.