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Omni-MATH / Mark and William are playing a game. Two walls are placed 1 meter apart, with…

Problem

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problem

Mark and William are playing a game. Two walls are placed 1 meter apart, with Mark and William each starting an orb at one of the walls. Simultaneously, they release their orbs directly toward the other. Both orbs are enchanted such that, upon colliding with each other, they instantly reverse direction and go at double their previous speed. Furthermore, Mark has enchanted his orb so that when it collides with a wall it instantly reverses direction and goes at double its previous speed (William's reverses direction at the same speed). Initially, Mark's orb is moving at \frac{1}{1000} meters/s, and William's orb is moving at 1 meter/s. Mark wins when his orb passes the halfway point between the two walls. How fast, in meters/s, is his orb going when this first happens?

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Source and history

task_id
d2a48c00-1b32-55a9-89a0-9537ffd200cc
task_key
test--d2a48c00-1b32-55a9-89a0-9537ffd200cc
task_revision_id
1
config / split
/ test

Official source

initial import