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 defined as the change in an object's momentum (\(\Delta p\)). According to the impulse-momentum theorem, the impulse applied to a skater equals the change in her momentum. By Newton's third law, this is also equal in magnitude to the impulse applied to the Frisbee. The objective is to identify the scenario resulting in the largest change in the Frisbee's momentum. Let the initial momentum of the Frisbee be \(p_i = mv\).
Step 2: Analyze momentum change for each scenario. - Case 1 (Catches and holds): The Frisbee's final momentum, \(p_f\), is incorporated into the skater's system. The momentum change is \(\Delta p = p_f - p_i\). The impulse required to stop the Frisbee relative to the skater is \(0 - mv = -mv\). The magnitude of this impulse is \(|mv|\). - Case 2 (Catches and drops): The horizontal impulse is identical to Case 1, as the skater must first absorb the Frisbee's momentum to make the catch. The magnitude is \(|mv|\). - Case 3 (Catches and throws back): The skater initially absorbs the momentum \(mv\) and then exerts an additional impulse to propel it backward, resulting in a final momentum \(p_f = -mv'\) (in the opposing 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 exceeds \(|mv|\). - Case 4 (Can't catch): If there is no interaction, the impulse is zero.
Step 3: Compare the impulses. The most significant change in momentum occurs when the Frisbee's velocity is reversed. This action imparts the largest impulse to the skater.