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Valter edited Sep 3, 2026, 6:34 PM

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		+	### Statement
		+
		+	$2.2.6.$ [Insert the problem statement]
		+
		+	### Solution
		+
		+	### Statement
		+
		+	$2.2.6.$ Sisters are standing on ice skates on smooth ice. The older one pushes the younger one. Both start rolling, but the younger one with a noticeably greater speed than the older one. "Let me push you now," says the younger one. Contrary to her expectations, she again rolls back with a greater speed than the older sister, and by the same factor as before. Why does this happen?
		+
		+	### Solution
		+
		+	From the law of conservation of momentum:
		+	$$\vec{p}_1 + \vec{p}_2 = \vec{0}$$
		+	$$m_1 v_1 = m_2 v_2$$
		+	$$v_1/v_2 = m_2/m_1$$
		+	From the resulting expression, it is clear that the speeds of the sisters will always relate as the inverse ratio of their masses.
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

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			### Statement

			$2.2.6.$ [Insert the problem statement]

			### Solution

			### Statement

			$2.2.6.$ Sisters are standing on ice skates on smooth ice. The older one pushes the younger one. Both start rolling, but the younger one with a noticeably greater speed than the older one. "Let me push you now," says the younger one. Contrary to her expectations, she again rolls back with a greater speed than the older sister, and by the same factor as before. Why does this happen?

			### Solution

			From the law of conservation of momentum:
			$$\vec{p}_1 + \vec{p}_2 = \vec{0}$$
			$$m_1 v_1 = m_2 v_2$$
			$$v_1/v_2 = m_2/m_1$$
			From the resulting expression, it is clear that the speeds of the sisters will always relate as the inverse ratio of their masses.

			#### Answer

			[Insert a concise answer or boxed result]