Question

two ice skaters stand facing each other at rest on a frozen pond. they push off against one another and the 48 kg skater acquires a speed of 0.73 m/s. if the other skater acquires a speed of 0.86 m/s, what is her mass in kilograms? kg

Explanation:

Step1: Apply the law of conservation of momentum

The initial momentum of the system is \(0\) (since both skaters are at rest initially). According to the law of conservation of momentum \(m_1v_1 + m_2v_2=0\), where \(m_1 = 48\space kg\), \(v_1=0.73\space m/s\), \(v_2 = - 0.86\space m/s\) (opposite direction).

Step2: Solve for \(m_2\)

From \(m_1v_1+m_2v_2 = 0\), we can express \(m_2\) as \(m_2=\frac{-m_1v_1}{v_2}\). Substitute the values: \(m_2=\frac{-48\times0.73}{- 0.86}\)

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Answer:

\(40.7\space kg\)