# Problem № 6 (10 points)

Five identical balls are rolling towards each other on a smooth horizontal surface. The speeds of the first and second are \( v_{1} = v_{2} = 0.5 \) m/s, while the others are \( v_{3} = v_{4} = v_{5} = 0.1 \) m/s. The initial distances between the balls are the same, \( l = 2 \) m. All collisions are perfectly elastic. How much time will pass between the first and last collisions in this system?

![](https://cdn.mathpix.com/cropped/2024_05_06_3676ffec89688f4f2c70g-6.jpg?height=183&width=277&top_left_y=702&top_left_x=221)

1

![](https://cdn.mathpix.com/cropped/2024_05_06_3676ffec89688f4f2c70g-6.jpg?height=162&width=272&top_left_y=707&top_left_x=595)

2

![](https://cdn.mathpix.com/cropped/2024_05_06_3676ffec89688f4f2c70g-6.jpg?height=166&width=254&top_left_y=705&top_left_x=935)

3

![](https://cdn.mathpix.com/cropped/2024_05_06_3676ffec89688f4f2c70g-6.jpg?height=171&width=297&top_left_y=700&top_left_x=1279)

4

![](https://cdn.mathpix.com/cropped/2024_05_06_3676ffec89688f4f2c70g-6.jpg?height=186&width=365&top_left_y=701&top_left_x=1665)

5

## Time: 10 min

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