Answer:
-7.14285 m/s
500 kgm/s
Explanation:
[tex]m_1[/tex] = Mass of light girl = 50 kg
[tex]m_2[/tex] = Mass of heavy girl = 70 kg
[tex]v_1[/tex] = Velocity of light girl = 10 m/s
[tex]v_2[/tex] = Velocity of heavy girl
As the momentum of the system is conserved
[tex]m_1v_1+m_2v_2=0\\\Rightarrow v_2=-\frac{m_1v_1}{m_2}\\\Rightarrow v_2=\frac{50\times 10}{70}\\\Rightarrow v_2=-7.14285\ m/s[/tex]
The velocity of the larger girl is -7.14285 m/s
Impulse is give by
[tex]J_1=m_1v_1\\\Rightarrow J_1=50\times 10\\\Rightarrow J_1=500 kgm/s[/tex]
[tex]J_1=m_1v_1\\\Rightarrow J_1=70\times -7.14285\\\Rightarrow J_1=-499.995\approx -500\ kgm/s[/tex]
The impulse that each girl exerts on each other is 500 kgm/s but the direction is opposite.
The reaction on the larger girl is that she reaches a velocity of -7.14 m/s, the impulse on the smaller girl is 500 kg*m/s, and the impulse on the larger girl is -500 kg*m/s.
Newton's third law says that every action has a reaction of equal magnitude but in the opposite direction.
When the larger girl pushes the smaller, she accelerates the smaller girl so she reaches a speed of 10.0 m/s, and she is also accelerated with the same force but in the opposite direction.
Remember, that, by the second law, force is equal to mass times acceleration.
Then the velocity of the larger girl is given by:
v = -10m/s*(50kg/70kg) = -7.14 m/s.
The impulse is given by the product between the mass and the velocity.
For the smaller girl, the impulse is:
I = (10m/s)*50kg = 500 m*kg/s
For the larger girl, the impulse is:
I' = (-7.14 m/s)*(70kg) = -500 m*kg/s
If you want to learn more about forces, you can read:
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