The impact velocity is 14.14 m s-1, derived from square root of two g h. Total kinetic energy equals 150 J, which divided by 3000 N resistive force gives a sand depression depth of 0.05 m.
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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Using conservation of energy, the velocity before impact equals square root of two times g times h, which is square root of 200, giving 14.14 m s-1. The kinetic energy on impact equals initial potential energy m g h, totaling 150 J. Equating this energy to work done against sand resistance, 150 J divided by 3000 N yields a depression depth of 0.05 m or 5 cm.
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