Questions: Recoil Momentum Two ice skaters are at rest, Abby and Ben. Abby has a mass of 52.5 kg. They push off each other. After, Abby moves 1.59 m / s east, while Ben moves 1.22 m / s west. What is Ben's mass? (Unit = kg) Remember: right is +, left is -

Solution Steps

We have two ice skaters, Abby and Ben, who push off each other and move in opposite directions. Abby's mass is given as \(52.5 \, \text{kg}\), and her velocity after the push is \(1.59 \, \text{m/s}\) east. Ben's velocity is \(1.22 \, \text{m/s}\) west. We need to find Ben's mass.

The law of conservation of momentum states that the total momentum before an event must equal the total momentum after the event, provided no external forces act on the system. Initially, both skaters are at rest, so the total initial momentum is zero.

The equation for conservation of momentum is:

\[ m_A \cdot v_A + m_B \cdot v_B = 0 \]

where:

• \(m_A = 52.5 \, \text{kg}\) is Abby's mass,
• \(v_A = 1.59 \, \text{m/s}\) is Abby's velocity,
• \(m_B\) is Ben's mass (unknown),
• \(v_B = -1.22 \, \text{m/s}\) is Ben's velocity (negative because it's west).

Substitute the known values into the momentum equation:

\[ 52.5 \cdot 1.59 + m_B \cdot (-1.22) = 0 \]

Simplify and solve for \(m_B\):

\[ 83.475 - 1.22 \cdot m_B = 0 \]

\[ 1.22 \cdot m_B = 83.475 \]

\[ m_B = \frac{83.475}{1.22} \]

\[ m_B \approx 68.4344 \, \text{kg} \]

Final Answer