Question

Two ice skaters want to prove conservation of momentum. Skater A has a mass of 72 kg, and skater B has a mass of 48 kg. They are originally at rest. They hold hands and face each other. They then push off each other and move in opposite directions. Skater B moves with a velocity of 3 m/s.What must the velocity of skater A be in the opposite direction after the push in order to prove conservation of momentum?

Answer 1

The initial momentum of the system can be expressed as,

$p_i=m_Au_A+m_Bu_B$

The final momentum of the system can be given as,

$p_f=m_Av_A+m_Bv_B$

According to conservation of momentum,

$p_i=p_f$

Substitute the known expressions,

$\begin{gathered} m_Au_A+m_Bu_{B_{}}=m_Av_A+m_Bv_B \\ m_Av_A=m_Au_A+m_Bu_B-m_Bv_B \\ v_A=\frac{m_Au_A+m_Bu_B-m_Bv_B}{m_A} \end{gathered}$

Substitute the known values in the equation,

$\begin{gathered} v_A=\frac{(72\text{ kg)(0 m/s)+(48 kg)(0 m/s)-(48 kg)(3 m/s)}}{72\text{ kg}} \\ =-\frac{(48\text{ kg)(3 m/s)}}{72\text{ kg}} \\ =-2\text{ m/s} \end{gathered}$

Thus, the magnitude of velocity of skater A in the opposite direction is 2 m/s.