Respuesta :
Given:
The mass of the 1st ball, m₁=0.500 kg
The velocity of the 1st ball before the collision, u₁=2.20 m/s
The mass of the 2nd ball, m₂=0.350 kg
The speed of the second ball before the collision, u₂=1.50 m/a
To find:
The velocities of the balls after the collision.
Explanation:
In an elastic collision, both momentum and the kinetic energies of the balls are conserved.
The velocities of the balls after the collision are given by,
[tex]\begin{gathered} v_1=\frac{m_1-m_2}{m_1+m_2}u_1+\frac{2m_2}{m_1+m_2}u_2\text{ }\to\text{ \lparen i\rparen} \\ v_2=\frac{2m_1}{m_1+m_2}u_1+\frac{m_2-m_1}{m_1+m_2}u_2\text{ }\to\text{ \lparen ii\rparen} \end{gathered}[/tex]Where v₁ is the velocity of the 1st ball and v₂ is the velocity of the 2nd ball.
On substituting the known values in equation (i),
[tex]\begin{gathered} v_1=\frac{0.500-0.350}{0.500+0.350}\times2.20+\frac{2\times0.350}{0.500+0.350}\times1.50 \\ =1.62\text{ m/s} \end{gathered}[/tex]On substituting the known values in the equation (ii),
[tex]\begin{gathered} v_1=\frac{2\times0.500}{0.500+0.350}\times2.20+\frac{0.350-0.500}{0.500+0.350}\times1.50 \\ =2.32\text{ m/s} \end{gathered}[/tex]Final answer:
The velocity of the 1st ball is 1.62 m/s after the collision.
The velocity of the 2nd ball after the collision is 2.32 m/s.
