Question

If the magnitude of a vector is 23, and the angle it makes with the x-axis is 32°, what is its horizontal vector component? Round all answers to the nearest hundredth.

Answer 1

The horizontal vector component of a vector with a magnitude of 23 that makes a 32° angle with the x-axis is approximately 19.52 when calculated using the cosine of the angle.

Step-by-step explanation:

The question asks for the horizontal component of a vector which has a magnitude of 23 and makes a 32° angle with the x-axis. To find the horizontal vector component, also known as the x-component, you can use the cosine function, which is part of the trigonometric relationship between the sides and angles of a right triangle. The formula for the x-component of a vector is:

Ax = A cos(θ)

where Ax is the horizontal component of the vector, A is the magnitude of the vector, and θ (theta) is the angle the vector makes with the x-axis.

Substituting the given values into the formula:

Ax = 23 cos(32°)

Using a calculator:

Ax ≈ 19.52 (rounded to the nearest hundredth)

Therefore, the horizontal vector component is approximately 19.52.