Answer:
0.78333 m/s in the opposite direction
1.566 m/s in the same direction
Explanation:
[tex]m_1[/tex] = Mass of penny = 0.0025 kg
[tex]m_2[/tex] = Mass of nickel = 0.005 kg
[tex]u_1[/tex] = Initial Velocity of penny = 2.35 m/s
[tex]u_2[/tex] = Initial Velocity of nickel = 0 m/s
[tex]v_1[/tex] = Final Velocity of penny
[tex]v_2[/tex] = Final Velocity of nickel
As momentum and Energy is conserved
[tex]m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}[/tex]
[tex]{\tfrac {1}{2}}m_{1}u_{1}^{2}+{\tfrac {1}{2}}m_{2}u_{2}^{2}={\tfrac {1}{2}}m_{1}v_{1}^{2}+{\tfrac {1}{2}}m_{2}v_{2}^{2}[/tex]
From the two equations we get
[tex]v_{1}=\frac{m_1-m_2}{m_1+m_2}u_{1}+\frac{2m_2}{m_1+m_2}u_2\\\Rightarrow v_1=\frac{0.0025-0.005}{0.0025+0.005}\times 2.35+\frac{2\times 0.5}{0.4005+0.5}\times 0\\\Rightarrow v_1=-0.78333\ m/s[/tex]
The final velocity of the penny is 0.78333 m/s in the opposite direction
[tex]v_{2}=\frac{2m_1}{m_1+m_2}u_{1}+\frac{m_2-m_1}{m_1+m_2}u_2\\\Rightarrow v_2=\frac{2\times 0.0025}{0.0025+0.005}\times 2.35+\frac{0.005-0.0025}{0.005+0.0025}\times 0\\\Rightarrow v_2=1.566\ m/s[/tex]
The final velocity of the nickel is 1.566 m/s in the same direction
