Maths & Physics Collection

As shown in the figure, There placed discus-shaped like small object at a height of h from the ground Throw at a muzzle velocity of Vo in the horizontal direction. It is known that when the block hits the ground and bounces in the vertical direction The ratio of the magnitude of the sub-velocity to the magnitude of the sub-velocity in the vertical direction of the leading edge of the collision is e(<1). Also know the coefficient of sliding friction between the block and the ground in the horizontal direction is μ (≠0) , the time of each collision process is very short, and it is all "flat surface"on the ground. Find the farthest distance the object block moves in the horizontal direction.

https://t.me/ProblemGalore0/1697 https://t.me/ProblemGalore0/1695

https://youtu.be/TrrfVHpqmUw?feature=shared BPhO weekly computational challenges for 2024 The INPhO dancing ball covered also the task discussed here was also appeared in CPhO I'll try to find that problem but in Chinese

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Try this problem:)

So be have to careful

Somewhere I feel it behaving like applied mechanics

Nice problem for JEE advanced maybe 🤷‍♂

Singapore Olympiad

Olyphy notes

Problem from Russian Olympiad

10 identical beads were put on an infinite vertical smooth spoke located in the gravitational field of the earth and launched with different initial speeds along the spoke. All blows are absolutely elastic. What is the maximum number of collisions that the beads can have in a long time (with optimization, you can vary the initial speeds and positions of the beads)

Here you've to consider length of spring at any time t

For part(2) I'll upload after 7feb But you guys have to do effort

Good solution by