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A hunter on a frozen, essentially frictionless pond uses a rifle that shoots 4.20 gg bullets at 970 m/sm/s. The mass of the hunter (including his gun) is 69.5 kgkg, and the hunter holds tight to the gun after firing it. You may want to review (Page) . For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Collision along a straight line. Part A Find the recoil speed of the hunter if he fires the rifle horizontally.

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Answer:

[tex]0.059\ \text{m/s}[/tex]

Explanation:

[tex]m_1[/tex] = Mass of bullet = 4.2 g

[tex]u_1[/tex] = Initial velocity of bullet = 0

[tex]m_2[/tex] = Mass of hunter with rifle = 69.5 kg

[tex]u_2[/tex] = Initial velocity of hunter with rifle

[tex]v_1[/tex] = Final velocity of the bullet = 970 m/s

[tex]v_2[/tex] = Final velocity of the hunter with the rifle

As the momentum of the system is conserved we have

[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow v_2=\dfrac{m_1u_1+m_2u_2-m_1v_1}{m_2}\\\Rightarrow v_2=\dfrac{0-0-0.0042\times 970}{69.5}\\\Rightarrow v_2=-0.059\ \text{m/s}[/tex]

The recoil speed of the hunter is [tex]0.059\ \text{m/s}[/tex] in the opposite direction of the bullet.

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