In Example 7.5, we considered an elastic collision in one dimension in which one of the objects is initially at rest. Notice that mass 2 is the one that is initially at rest. Use the results for v_1f and v_2f to answer the following problems. 

(a) Assume m₁ = 10m₂ so that the incoming object is much more massive than the one at rest. Find v_1f /v_1i and v_2f/v_1i. Explain why the final velocity of the smaller object is much larger (in magnitude) than the final velocity of the bigger object. 

(b) Assume m₁ = m₂ /10. Find v_1f /v_1i and v_2f /v_1i. Explain why the final velocity of the smaller object is opposite its initial direction.