Question

A force directed 51.8° below the positive x-axis has an x component of 4.93 lb. Find its y component.

Answer 1

y= 6.26 lb.

Step-by-step explanation:

1. Draw the vector of the force to better visualize and understand the problem.

Check attached image 1.

2. Find an expression for the force in the y axis.

Using the trigonometric functions, we need to find a function that relates the angle, opposite side and adjacent side of the drawn triangle. The function that does this is the tangent.

Let theta (θ) be the angle given by the problem.

Let "y" be the missing y component.

Tangent (θ) = Opposite side (y) / Adjacent side (x)

`Tan(tetha)=(y)/(x)`

3. Solve the equation for y by multiplying both sides by x.

`Tan(tetha)*x=y`

4. Substitute the information given by the problem and calculate y.

`Tan(51.8)*(4.93)=y\\ \\y=6.26`

5. Express the result.

y= 6.26 lb.