Question

A skater is using very low-friction rollerblades. A friend throws a Frisbee straight at her. In which case does the Frisbee impart the greatest impulse to the skater:

• A. she catches the Frisbee and holds it
• B. she catches it momentarily but drops it
• C. she catches it and at once throws it back to her friend
• D. she cant catch it at all

Hint:

Impulse is maximized when there is a reversal of momentum. Think of a bouncy ball versus a lump of clay hitting a wall; the bouncy ball imparts a greater impulse because its momentum changes from \(+p\) to \(-p\), a total change of \(2p\).

Answer 1

The Correct Option is C

Step 1: Define impulse. Impulse is the change in momentum of an object (\(\Delta p\)). By the impulse-momentum theorem, the impulse imparted to the skater is equal to the change in her momentum. By Newton's third law, this is equal in magnitude to the impulse imparted to the Frisbee. We need to find the case with the largest change in the Frisbee's momentum. Let the initial momentum of the Frisbee be \(p_i = mv\).
Step 2: Analyze the change in momentum for each case. - Case 1 (Catches and holds): The Frisbee's final momentum, \(p_f\), becomes part of the skater's system. The change in momentum is \(\Delta p = p_f - p_i\). The impulse to stop the Frisbee relative to the skater is \(0 - mv = -mv\). The magnitude is \(|mv|\). - Case 2 (Catches and drops): The horizontal impulse is the same as in case 1, as the skater must first absorb the Frisbee's momentum to catch it. The magnitude is \(|mv|\). - Case 3 (Catches and throws back): The skater first absorbs the initial momentum \(mv\) and then imparts an additional momentum to throw it back, giving it a final momentum \(p_f = -mv'\) (in the opposite direction). The total change in the Frisbee's momentum is \(\Delta p = p_f - p_i = (-mv') - (mv) = -m(v+v')\). The magnitude of the impulse is \(m(v+v')\), which is larger than \(|mv|\). - Case 4 (Can't catch): No interaction means zero impulse.
Step 3: Compare the impulses. The greatest change in momentum occurs when the Frisbee's velocity is reversed. This action imparts the largest impulse to the skater.