 Solution

ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/section-b/6/g/solution

For actual complete bounce distances

D_{1} = 4 m

and

D_{n + 1} = r D_{n}

D_{total} = \frac{4}{1 - r} m, 0 \leq r < 1.

A natural intended estimate compares the observed first round trip with the loss-free round trip from the initially compressed position,

D_{ideal} = 2 (H_{s} + x) = 5.13764 m .

If the reduction factor is taken to be

r = D_{1} / D_{ideal} = 0.77857

, the answer is $D_{total} ≃ 18.1 m$ . The first term is the actual 4 m, not the hypothetical loss-free distance.

This numerical inference needs the stated comparison assumption. Strictly, knowing the first actual bounce distance and saying subsequent distances share a ratio does not independently specify that ratio. A change in spring compression also means that an energy-loss fraction is not automatically the same as a vertical-distance ratio.

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