The final velocity of the first ball after the collision is 1.167 m/s to the west.
The given parameters;
Let the velocity of the first ball after collision = v₁
Let the velocity of the ball at rest after collision = v₂
Apply the principle of conservation of linear momentum;
[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\\\\0.4(3.7)+ 0.2(0) = 0.4(-v_1) + 0.2v_2\\\\1.48 = -0.4v_1 + 0.2v_2[/tex]
Apply one-directional velocity formula;
[tex]u_1 + v_1 = u_2 + v_2\\\\3.7 - v_1 = 0 + v_2\\\\v_2 = 3.7 -v_1[/tex]
substitute the value of v₂ into the above equation;
[tex]1.48 = -0.4v_1 \ + \ 0.2(3.7 -v_1)\\\\1.48 = -0.4v_1 + 0.74 - 0.2v_1\\\\0.74 = -0.6v_1\\\\v_1 = \frac{-0.74}{0.6} \\\\v_1 = -1.167 \ m/s[/tex]
[tex]v_2 = 3.7 + 1.167\\\\v_2 = 4.867 \ m/s[/tex]
Thus, the final velocity of the first ball after the collision is 1.167 m/s to the west.
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