Solution:
Let \(m_A = 2m_R\). Given \(K_A = \frac{1}{3}K_R ⇒ \frac{1}{2}m_A v'^2 = \frac{1}{3}\left(\frac{1}{2}m_R v^2\right)\). Substituting \(m_A = 2m_R\), we get \(2v'^2 = \frac{1}{3}v^2 ⇒ v' = \frac{v}{\sqrt{6}}\).
Let \(m_A = 2m_R\). Given \(K_A = \frac{1}{3}K_R ⇒ \frac{1}{2}m_A v'^2 = \frac{1}{3}\left(\frac{1}{2}m_R v^2\right)\). Substituting \(m_A = 2m_R\), we get \(2v'^2 = \frac{1}{3}v^2 ⇒ v' = \frac{v}{\sqrt{6}}\).
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