Question

You walk in a straight line for 95 m at an angle of 162° above the positive x-axis. What are the x and y components of your displacement?

Answer 1

To find the x and y components of the displacement when walking 95 m at an angle of 162° above the positive x-axis, we can use trigonometric functions.

The x-component can be calculated using the cosine function, and the y-component can be calculated using the sine function.

1. **Calculate the x-component**:
\[
x = r \cdot \cos(\theta)
\]
where \( r = 95 \) m and \( \theta = 162^\circ \).

\[
x = 95 \cdot \cos(162^\circ)
\]

2. **Calculate the y-component**:
\[
y = r \cdot \sin(\theta)
\]

\[
y = 95 \cdot \sin(162^\circ)
\]

Now, we can calculate the values:

- **x-component**:
\[
x = 95 \cdot \cos(162^\circ) \approx 95 \cdot (-0.9239) \approx -87.76 \text{ m}
\]

- **y-component**:
\[
y = 95 \cdot \sin(162^\circ) \approx 95 \cdot 0.3827 \approx 36.36 \text{ m}
\]

Therefore, the x and y components of the displacement are:
- \( x \approx -87.76 \, \text{m} \)
- \( y \approx 36.36 \, \text{m} \)

Final answer:
- \( x \approx -87.76 \, \text{m} \)
- \( y \approx 36.36 \, \text{m} \)