3. A ball sliding on a smooth horizontal surface catches up with a block moving along the same surface. The ball's velocity is perpendicular to the edge of the block, against which it collides. The mass of the ball is much less than the mass of the block. After an elastic collision, the ball slides along the surface in the opposite direction with a speed that is half of its initial speed.

Find the ratio of the ball's and the block's velocities before the collision.
3. Law of velocity addition:

$$
\begin{array}{cl}
(V-U)-U=\frac{1}{2} V ; & V\left(1-\frac{1}{2}\right)=2 U \\
\frac{V}{2}=2 U ; & \frac{V}{U}=4
\end{array}
$$

![](https://cdn.mathpix.com/cropped/2024_05_06_556368b0f812d0b7a511g-3.jpg?height=349&width=645&top_left_y=1810&top_left_x=1274)