Two ice skaters with masses of 77 kg and 55 kg stand facing

Two ice skaters, with masses of 77 kg and 55 kg, stand facing each other on a 13-m-wide frozen river. The skaters push off against each other glide backward straight toward the river\'s edges, and reach the edges at exactly the same time. How far did the 77 kg skater glide? Express your answer to two significant figures and include the appropriate

Solution

By Conservation of momentum

m_AV_A=m_BV_B

77V_A=55V_B

V_B=(77/55)V_A

Given t_A=t_B=t

X_B/t =(7/5)(X_A/t)

X_B=(7/5)X_A

_Given

X_A+X_B=13

X_A+(7/5)X_A =13

2.4X_A=13

X_A=5.42 m