Question

If the magnitude of a vector is 23 and the angle it makes with the x-axis is 32 degrees, what is its horizontal vector component?

A) 18.6
B) 20.1
C) 12.3
D) 14.7

Answer 1

The horizontal component of a vector with a magnitude of 23 and an angle of 32 degrees is found using the cosine of the angle. After calculation, it is approximately 19.5, which most closely matches multiple-choice option B (20.1).

Step-by-step explanation:

To find the horizontal component of a vector (also known as the x-component), we use the cosine function because the x-component is adjacent to the angle when the vector is represented in a right-angled triangle. The formula is Ax = A cos(\theta), where Ax is the horizontal component, A is the magnitude of the vector, and \theta is the angle with the x-axis.

Given a vector with a magnitude of 23 and an angle of 32 degrees, we calculate the horizontal component as follows:

• Ax = 23 cos(32°)
• Ax = 23 * 0.848 (cosine of 32 degrees is approximately 0.848)
• Ax = 19.504

Therefore, the horizontal component is approximately 19.5, which is closest to option B (20.1) if we are selecting from a multiple-choice list.