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In principle, when you fire a rifle, the recoil should push you backward. How big a push will it give? Let’s find out by doing a calculation in a very artificial situation. Suppose a man standing on frictionless ice fires a rifle horizontally. The mass of the man together with the rifle is 70 kg, and the mass of the bullet is 10 g. If the bullet leaves the muzzle at a speed of 500 m/s, what is the final speed of the man? Given your result, do you expect to be pushed backward when you fire a rifle?

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Answer:

0.07142 m/s in the opposite direction of the bullet

Explanation:

[tex]m_1[/tex] = Mass of rifle = 70 kg

[tex]m_2[/tex] = Mass of bullet = 0.01 kg

[tex]v_1[/tex] = Velocity of rifle

[tex]v_2[/tex] = Velocity of bullet = 500 m/s

As the momentum of the system is conserved

[tex]m_1v_1+m_2v_2=0\\\Rightarrow v_1=-\frac{m_2v_2}{m_1}\\\Rightarrow v_1=-\frac{0.01\times 500}{70}\\\Rightarrow v_1=-0.07142\ m/s[/tex]

The recoil velocity of the rifle is -0.07142 m/s

The negative sign shows the opposite direction of the rifle.

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