17.5kg Olivia is running to Elizabeth who is standing still with a velocity of 8 ms and jumps into her arms to be held if Elizabeths mass is 68 kg what is their final velocity

We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the two girls must be conserved before and after the collision.

Therefore we can write:

[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v[/tex]

where:

[tex]m_1 = 17.5 kg[/tex] is the mass of Olivia

[tex]u_1 = 8 m/s[/tex] is the initial velocity of Olivia

[tex]m_2 = 68 kg[/tex] is the mass of Elizabeth

[tex]u_2 = 0[/tex] is the initial velocity of Elizabeth

[tex]v[/tex] is the final combined velocity of the two girls

Re-arranging the equation and substituting the values, we find the final velocity:

[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(17.5)(8)+0}{17.5+68}=1.64 m/s[/tex]

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