Respuesta :
Answer:
The velocity of the first person is 2.9795 m/s and the velocity of the second person is 0.0275 m/s
Explanation:
First, we are going to study the interacción between the ball and the first person. In every case the linear momentum is conserved so:
[tex]m_1v_{i1} +m_bv_{ib}=m_1v_{f1}+m_bv_{b}[/tex]
Where [tex]m_1[/tex] is the mass of the first person, [tex]m_b[/tex] is the mass of the ball, [tex]v_{i1}[/tex] and [tex]v_{f1}[/tex] are the initial and final velocities of the first person, [tex]v_{ib}[/tex] is the initial velocities of the ball and [tex]v_{b}[/tex] is the velocity of the ball once it is throws.
So, if we replace the values and solve for [tex]v_{f1}[/tex], we get:
[tex]69.5Kg(3m/s)+(0.0445Kg)(3m/s)=(69.5kg)v_{f1}+(0.0445)(35m/s)[/tex]
[tex]208.6335=69.5v_{f1}+1.5575[/tex]
[tex]\frac{208.6335-1.5575}{69.5}=v_{f1}\\2.9795=v_{f1}[/tex]
Therefore, the velocity of the first person after the snowball is exchanged is 2.9795 m/s
Now, we are going to study the interaction between the ball and the second person, we get:
[tex]m_2v_{i2} +m_bv_{b}=m_2v_{f2}+m_bv_{fb}[/tex]
Where [tex]m_2[/tex] is the mass of the second person, [tex]v_{i2}[/tex] is the initial velocity of the second person, [tex]v_{f2}[/tex] is the final velocity of the second person and [tex]v_{fb}[/tex] is the final velocity of the ball.
[tex]v_{f2}[/tex] is equal to [tex]v_{fb}[/tex], so if we replace the values and solve for [tex]v_{f2}[/tex], we get:
[tex](56.5kg)(0 m/s)+(0.0445)(35)=(56.5Kg)v_{f2}+(0.0445Kg)v_{f2}[/tex]
[tex]1.5575=(56.5445)v_{f2}[/tex]
[tex]\frac{1.5575}{56.5445} =v_{f2}\\0.0275=v_{f2}[/tex]
Finally, the the velocity of the second person after the snowball is exchanged is 0.0275 m/s
