Question

PRACTICE PROBLEM

3. A displacement vector 7 has a magnitude of r= 175 m and points at an angle of 50.0° relative to the x-axis in Figure 2.27. Find the x-and
-components of this vector.
50.0°
α
90.0%
ta
X
FIGURE 2.27 Problem 3.

Answer 1

To find the x- and y-components of the vector, we can use trigonometric functions. The x-component is the adjacent side of the angle and the y-component is the opposite side.

Given:

Magnitude r = 175 m

Angle α = 50.0°

The x-component can be found using the cosine function:

cos(α) = adjacent/hypotenuse

cos(50.0°) = x/175

x = 175 cos(50.0°)

x ≈ 112.25 m

The y-component can be found using the sine function:

sin(α) = opposite/hypotenuse

sin(50.0°) = y/175

y = 175 sin(50.0°)

y ≈ 135.55 m

Therefore, the x-component of the vector is approximately 112.25 m and the y-component is approximately 135.55 m.