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An Arrow (1 kg) travels with velocity 30 m/s to the right when it pierces an apple (2 kg) which is initially at rest. After the collision, the arrow and the apple are stuck together. Assume that no external forces are present and therefore the momentum for the system is conserved. What is the final velocity (in m/s) of apple and arrow after the collision?

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boffeemadrid

Answer:

10 m/s

Explanation:

[tex]m_1[/tex] = Mass of arrow = 1 kg

[tex]m_2[/tex] = Mass of apple = 2 kg

[tex]u_1[/tex] = Initial Velocity of arrow = 30 m/s

[tex]u_2[/tex] = Initial Velocity of apple = 0 m/s

[tex]v[/tex] = Velocity of combined mass

For elastic collision

[tex]m_1u_1 + m_2u_2 =(m_1 + m_2)v\\\Rightarrow v=\frac{m_1u_1 + m_2u_2}{m_1 + m_2}\\\Rightarrow  v=\frac{1\times 30 + 2\times 0}{1 + 2}\\\Rightarrow v=10\ m/s[/tex]

Final velocity of apple and arrow after collision is 10 m/s

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