Answer:
To find the y-component of the vector \( \mathbf{V} \), you can use the following formula:
\[
V_y = V \sin(\theta)
\]
where:
- \( V \) is the magnitude of the vector.
- \( \theta \) is the angle the vector makes with the positive x-axis.
- \( V_y \) is the y-component of the vector.
Given:
- \( V = 55.1 \, \text{m} \)
- \( \theta = 76.1^\circ \)
Substitute these values into the formula:
\[
V_y = 55.1 \sin(76.1^\circ)
\]
Using a calculator to find the sine of \( 76.1^\circ \):
\[
\sin(76.1^\circ) \approx 0.9703
\]
Now, calculate \( V_y \):
\[
V_y = 55.1 \times 0.9703 \approx 53.4
\]
So, the y-component \( V_y \) is approximately \( 53.4 \, \text{m} \).