Recoil on ice

Problem

Estimate the recoil velocity of a $70\;\mathrm{kg}$ person standing on a frictionless icy surface when they throw a basketball ($0{,}6\;\mathrm{kg}$) horizontally at a typical throwing speed.

Solution

This is a Fermi estimate. First I need a typical throwing speed: a two-handed pass is made at about $v_p \sim 10$–$12\;\mathrm{m/s}$; I assume $v_p \approx 12\;\mathrm{m/s}$. The person + ball system is initially at rest and there are no horizontal external forces (frictionless ice): the total horizontal momentum stays zero. This is effectively a two-body “explosion”. I call $M = 70\;\mathrm{kg}$ (person), $m = 0{,}6\;\mathrm{kg}$ (ball), $V$ the recoil velocity: $0 = M\,V - m\,v_p \;\Rightarrow\; V = \frac{m\,v_p}{M}$ Substituting: $V = \frac{0{,}6\;\mathrm{kg}\cdot 12\;\mathrm{m/s}}{70\;\mathrm{kg}} = \frac{7{,}2}{70}\;\mathrm{m/s} \approx 0{,}10\;\mathrm{m/s}$ The person recoils slowly, of the order of ten centimetres per second, in the direction opposite to the throw. $\ev{V \sim 10\;\mathrm{cm/s}}$

Links

Topics: Quantità di moto e urti Concepts: Conservazione della quantità di moto · Esplosione Skills: Stime di Fermi · Conservazione della quantità di moto