Respuesta :
Answer:
A. 6 m/s, 12 m/s
Explanation:
Given:
mass₁ (m₁) = 10 kg
initial velocity₁ (v₁) = 10 m/s
mass₂ (m₂) = 5 kg
initial velocity₂ (v₂) = 4 m/s
coefficient of restitution (e) = 1
Based on the Law of Conservation of Momentum:
[tex]\boxed{m_1v_1+m_2v_2=m_1v_1'+m_2v_2'}[/tex]
where v' is the final velocity.
Therefore:
[tex]10\times10+5\times4=10v_1'+5v_2'[/tex]
[tex]10v_1'+5v_2'=120[/tex]
[tex]2v_1'+v_2'=24\ ...\ [1][/tex]
Coefficient of Restitution formula:
[tex]\boxed{e=\frac{v_2'-v_1'}{v_1-v_2} }[/tex]
[tex]\displaystyle 1=\frac{v_2'-v_1'}{10-4}[/tex]
[tex]v_1'-v_2'=-6\ ...\ [2][/tex]
[1] & [2]
2v₁' + v₂' = 24
v₁' - v₂' = -6
--------------------- (+)
3v₁' = 18
v₁' = 6 m/s
[2]
v₁' - v₂' = -6
6 - v₂' = -6
v₂' = 12 m/s
Final answer:
In an elastic collision, conservation of momentum and kinetic energy yields the final velocities of the two balls as 6 m/s and 12 m/s, respectively, making option A the correct answer.
Explanation:
The subject of this question is a typical Physics problem involving elastic collisions in one dimension. When dealing with elastic collisions, both momentum and kinetic energy are conserved. To solve the problem, we can set up two equations: one for the conservation of momentum and one for the conservation of kinetic energy.
Conservation of momentum before and after collision can be expressed as:
m1*v1_initial + m2*v2_initial = m1*v1_final + m2*v2_final
For conservation of kinetic energy:
0.5*m1*(v1_initial)^2 + 0.5*m2*(v2_initial)^2 = 0.5*m1*(v1_final)^2 + 0.5*m2*(v2_final)^2
For the given problem, we would use:
- m1 = 10 kg, v1_initial= 10 m/s
- m2 = 5 kg, v2_initial = 4 m/s
Plugging these values into the equations, solving for v1_final and v2_final will give us the final velocities of both balls post-collision. In this case, using the conservation laws and solving the system of equations yields the final velocities as 6 m/s for the first ball and 12 m/s for the second ball, which corresponds to option A.
