8. (15 points) A rigid rod is moving on a horizontal table. At a certain moment, the speed of one end of the rod is \( v_{1}=10 \mathrm{M} / \mathrm{c} \), and the speed of the other end is \( v_{2}=6 \mathrm{M} / \mathrm{c} \) and it is directed along the axis of the rod (see figure). Determine the speed of the midpoint of the rod at this moment.

![](https://cdn.mathpix.com/cropped/2024_05_06_32f4aa6e8cb387df1c88g-10.jpg?height=177&width=980&top_left_y=962&top_left_x=618)
Answer: $\approx 7.2 \mu / c$

Solution. All points on the rod have a velocity component directed to the right, equal to $v_{2}$.

(4 points)

Therefore, the velocity component directed upwards for point A: $v_{\text {vert } A}=\sqrt{v_{1}^{2}-v_{2}^{2}}=8 \mathrm{M} / \mathrm{c}$.

The velocity component of point $B$, directed upwards:

$v_{\text {vert } B}=\frac{1}{2} v_{\text {vert } A}=4 \mathrm{M} / c$.

The total velocity of point $B: v=\sqrt{v_{2}^{2}+v_{\text {vert } B}^{2}}=\sqrt{6^{2}+4^{2}} \approx 7.2 \mathrm{M} / \mathrm{c}$.