Question

A standard rifle has a mass of 2.68 kilograms. If it were used to fire an “elephant gun” round of mass 69.5 grams at +612 meters per second, what would be the recoil velocity of the rifle? Answer must be in 3 significant digits.

Answer 1

We have

mr=mass rifle

mb=mass bullet

vb0=initial velocity of the bullet

vr0=initial velocity of the rifle

vbf=final velocity of the bullet

vrf=final velocity of the rifle

mr=2.68 kg

mb=69.5 g =0.0695 kg

vb0=0 m/s

vr0=0m/s

vbf=612 m/s

vrf=?

`m_bv_(bo)+m_rv_(ro)=m_bv_(bf)+m_rv_(rf)`

`0=m_bv_(bf)+m_rv_(rf)`

we isolate the vr

`v_(rf)=(-m_bv_(bf))/(m_r)`

Then we substitute

The recoil velocity is -15.871 m/s