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A coconut of mass 1.5 kg falls from the top of a coconut tree onto the wet sand on a beach. The height of the tree is 10 m. On impact, the coconut comes to rest by making a depression in the sand. (i) Calculate the velocity of the coconut just before it hits the sand. (ii) Assume that the average resistive force of sand is 3000 N and all of the coconut's energy is used to create the depression in the sand. Calculate the depth of the depression the coconut makes in the sand. Assume g = 10 m s⁻².
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(i) \(v = \sqrt{2gh} = \sqrt{2 \times 10 \times 10} = \sqrt{200} \approx 14.1\ \text{m s}^{-1}\).
(ii) Energy at impact \(= mgh = 1.5 \times 10 \times 10 = 150\ \text{J}\). This equals work done against the sand \(= F \times d\):
\( 3000 \times d = 150 \Rightarrow d = 0.05\ \text{m} = 5\ \text{cm} \).
