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 0.71 m/s. if the other skater acquires a speed of 0.85 m/s, what is her mass in kilograms? kg resources reading

Explanation:

Step1: Apply the law of conservation of momentum

The initial momentum of the system (two skaters) is \(0\) since they are at rest (\(p_{initial}=0\)). According to the law of conservation of momentum \(p_{initial} = p_{final}\), so \(m_1v_1+m_2v_2 = 0\), which can be rewritten as \(m_1v_1=-m_2v_2\). Here, we can take magnitudes (\(\vert m_1v_1\vert=\vert m_2v_2\vert\)) because we are interested in the mass - speed relationship. Let \(m_1 = 48\space kg\), \(v_1=0.71\space m/s\) and \(v_2 = 0.85\space m/s\).

Step2: Solve for \(m_2\)

From \(\vert m_1v_1\vert=\vert m_2v_2\vert\), we can express \(m_2=\frac{m_1v_1}{v_2}\). Substitute the given values: \(m_2=\frac{48\times0.71}{0.85}\).
First, calculate \(48\times0.71 = 34.08\). Then, \(\frac{34.08}{0.85}=40.094118\approx40.1\space kg\)

Answer:

\(40.1\)