Question

The collision between a geological hammer and a rock lying loose on the ground can be considered to be approximately elastic.

Answer 1

Answer

given,

mass of the rock ( m ) = 0.21 Kg

mass of hammer ( M ) = 0.55 Kg

initial speed of the hammer ( u ) =  5.2 m/s

final speed of the rock = ?

using energy of conservation

$Mu = M v + m v'$.....(1)

In elastic collision Kinetic energy is equal to final energy

$\dfrac{1}{2}Mu^2 = \dfrac{1}{2}Mv^2 + \dfrac{1}{2}Mv'^2$....(2)

on solving both the equation for velocity of hammer

$v' = \dfrac{M-m}{M+m}u$

$v' = \dfrac{0.55-0.21}{0.55+0.21}\times 5.2$

v' = 2.33 m/s

velocity of the rock

$v = \dfrac{2M}{M+m}v'$

$v = \dfrac{2\times 0.55}{0.55 + 0.21}\times 2.33$

v = 3.37 m/s