The final velocity is 3.47 m/s east
Explanation:
We can solve this problem by using the law of conservation of momentum. In fact, the total momentum of the two players before and after the collision must be conserved:
[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v[/tex]
where:
[tex]m_1 = 91.5 kg[/tex] is the mass of the first player
[tex]u_1 = 3.73 m/s[/tex] is the initial velocity of the first player (we take east as positive direction)
[tex]m_2 = 63.5 kg[/tex] is the mass of the second player
[tex]u_2 = 3.09 m/s[/tex] is the initial velocity of the second player
[tex]v[/tex] is their final combined velocity after the collision
Re-arranging the equation and substituting the values, we find:
[tex]v = \frac{m_1 u_1+m_2 u_2}{m_1+m_2}=\frac{(91.5)(3.73)+(63.5)(3.09)}{91.5+63.5}=3.47 m/s[/tex]
So, their velocity afterwards is 3.47 m/s east.
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