hunter, shoot yourself · Physics Brawl 2022 #4

Physics · mechanics

Problem

What is the largest radius a planet can have for a person to be able to shoot oneself on it? Hunter shoots just above its surface, parallel to it, and the planet will have no atmosphere. The velocity of a flying bullet is v=380v = 380 m·s⁻¹, and the density of the planet is ρ=3200\rho = 3200 kg·m⁻³. Furthermore, assume the planet to be spherical and homogeneous.

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