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Two identical balls, \( A \) and \( B \), undergo a perfectly elastic two dimensional collision. Initially, \( A \) is moving with a speed of \( 10 \mathrm{~m} / \mathrm{s} \) and \( B \) is at rest. Due to collision, \( A \) is scattered through an angle of \( 30^{\circ} \). What are the speeds of \( A \) and \( B \) after the collision?
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