This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

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Let and be the masses of spheres A and B, respectively. Let and be their initial velocities (taking the direction of A as positive). Let and be their velocities after impact.
i) Find in terms of and the speeds of A and B after impact.
Step 1: Apply the principle of conservation of momentum.
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You're right to check your work! Let's go through it step-by-step to find the correct expressions for v_A and v_B.
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.