A vector representing 190 N is oriented at 47◦

with the horizontal.
What is the magnitude of its horizontal
component?

190cos47 N (the N stands for Newtons)

Do the math

To find the magnitude of the horizontal component of the vector, we can use trigonometric functions. The horizontal component can be found using the cosine function.

The formula to find the horizontal component is:

Horizontal component = Magnitude of the vector * cos(angle)

Given that the magnitude of the vector is 190 N and the angle with the horizontal is 47°, we can substitute these values into the formula:

Horizontal component = 190 N * cos(47°)

Using a calculator, we can find the cosine of 47°:

cos(47°) ≈ 0.682

Substituting this value back into the formula:

Horizontal component = 190 N * 0.682

Horizontal component ≈ 129.98 N

Therefore, the magnitude of its horizontal component is approximately 129.98 N.

To find the magnitude of the horizontal component of a vector, you can use trigonometry. In this case, you know the magnitude of the vector (190 N) and the angle it makes with the horizontal (47 degrees).

The horizontal component of a vector can be found using the formula:

Horizontal component = Magnitude of the vector * cos(angle)

In this case, plugging in the values:

Horizontal component = 190 N * cos(47 degrees)

Using a calculator:

Horizontal component ≈ 190 N * 0.682
Horizontal component ≈ 129.58 N

Therefore, the magnitude of the horizontal component of the vector is approximately 129.58 N.