Answer:
The final velocity of the car A is -1.053 m/s.
Explanation:
For an elastic collision both the kinetic energy and the momentum of the system are conserved.
Let us call
[tex]m_A[/tex] = mass of car A;
[tex]v_{A1}[/tex] = the initial velocity of car A;
[tex]v_{A2}[/tex] = the final velocity of car A;
and
[tex]m_B[/tex] = mass of car B;
[tex]v_{B1}[/tex] = the initial velocity of car B;
[tex]v_{B2}[/tex] = the final velocity of car B.
Then, the law of conservation of momentum demands that
[tex]m_Av_{A1}+m_Bv_{B1} =m_Av_{A2}+m_Bv_{B2}[/tex]
And the conservation of kinetic energy says that
[tex]\dfrac{1}{2} m_Av_{A1}^2+\dfrac{1}{2}m_Bv_{B1}^2=\dfrac{1}{2}m_Av_{A2}^2+\dfrac{1}{2}m_Bv_{B2}^2[/tex]
These two equations are solved for final velocities [tex]v_{A2}[/tex] and [tex]v_{B2}[/tex] to give
[tex]$v_{A2} =\frac{m_A-m_B}{m_A+m_B} v_{A1}+\frac{2m_B}{m_A+m_B} v_{B1}$[/tex]
[tex]$v_{B2} =\frac{2m_A}{m_A+m_B} v_{A1}+\frac{m_B-m_A}{m_A+m_B} v_{B1}$[/tex]
by putting in the numerical values of the variables we get
[tex]$v_{A2} =\frac{281-209}{281+209} (2.82)+\frac{2*209}{281+209} (-1.72)$[/tex]
[tex]\boxed{v_{A2} = -1.05m/s}[/tex]
and
[tex]$v_{B2} =\frac{2*281}{281+209} (2.82)+\frac{209-281}{281+209} (-1.72)$[/tex]
[tex]\boxed{v_{B2} = 3.49m/s}[/tex]
Thus, the final velocity of the car A is -1.053 m/s and of car B is 3.49 m/s.
The velocity of car A after collision is -1.05 m/s.
The given parameters:
The velocity of car A after collision is determined by applying the principle of conservation of linear momentum;
[tex]m_A v_A_1 + m_B v_B_1 = m_Av _A_2 + m_Bv_B_2\\\\281(2.82) + 209(-1.72) = 281(v_A_2) + 209v_B_2\\\\432.94 = 281(v_A_2) + 209v_B_2[/tex]
Apply one - dimensional velocity;
[tex]v_A_1 + v_A_2 = v_B_1 + v_B_2\\\\2.82 + v_A_2 = -1.72 + v_B_2\\\\2.82 + 1.72 + v_A_2 = v_B_2\\\\4.54 + v_A_2 = v_B_2[/tex]
[tex]432.94 = 281(v_A_2) + 209(4.54 + v_A_2)\\\\432.94 = 281v_A_2 + 948.86 + 209v_A_2\\\\-515.92 = 490v_A_2\\\\v_A_2 = \frac{-515.92}{490} \\\\v_A_2 = -1.05 \ m/s[/tex]
Thus, the velocity of car A after collision is -1.05 m/s.
Learn more about conservation of linear momentum here: https://brainly.com/question/7538238
