Answered

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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.

Sagot :

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=?

[tex]m_bv_{bo}+m_rv_{ro}=m_bv_{bf}+m_rv_{rf}[/tex]

[tex]0=m_bv_{bf}+m_rv_{rf}[/tex]

we isolate the vr

[tex]v_{rf}=\frac{-m_bv_{bf}}{m_r}[/tex]

Then we substitute

[tex]v_{rf}=\frac{-(0.0695\operatorname{kg})(612)}{2.68}=-15.871\text{ m/s}[/tex]

The recoil velocity is -15.871 m/s

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