We are given the following information:
Weight of skater 1 = 625 N
Weight of skater 2 = 725 N
Final velocity of skater 2 = 1.5 m/s
Final velocity of skater 1 = ?
Recall from the law of conservation of momentum, the total momentum before the collision and after the collision must be equal.
[tex]\begin{gathered} p_{before}=p_{after} \\ m_1u_1+m_2u_2=m_1v_1+m_2v_2 \end{gathered}[/tex]The initial velocities of both skaters are 0 m/s
[tex]m_1\cdot0_{}+m_2\cdot0=m_1v_1+m_2v_2[/tex]Also, m = W/g
[tex]\begin{gathered} 0=m_1v_1+m_2v_2 \\ 0=(\frac{625}{9.8})\cdot_{}v_1+(\frac{725}{9.8})\cdot1.5 \\ (\frac{625}{9.8})\cdot_{}v_1=-(\frac{725}{9.8})\cdot1.5 \\ (63.78)\cdot_{}v_1=-110.97 \\ _{}v_1=-\frac{110.97}{63.78} \\ _{}v_1=-1.7\: \frac{m}{s} \end{gathered}[/tex]So, the lighter skater will travel with a velocity of 1.7 m/s
The negative sign means that the lighter skater will be traveling oppositely to the heavier skater.
