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.
Calculate the velocity of the coconut just before it hits the sand.
Given: Mass, m = 1.5 kg; Height, h = 10 m; Initial velocity, u = 0; g = 10 m s⁻².
Formula: Using the equation of motion, v² = u² + 2gh
Calculation: v² = 0 + × 10 = 200
Result: v = = 10 m/s 14.14 m/s
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.
Given: Average resistive force, F = 3000 N
Energy of coconut: The total energy of the coconut just before hitting the sand is its potential energy at the top, E = mgh = × 10 = 150 J.
Formula: Work done by the resistive force = Energy of the coconut. So, F × d = mgh
Calculation: 3000 × d = 150
Result: d = 150 / 3000 = 0.05 m
Explanation
Part (i) uses the kinematic equation v² = u² + 2gh to find the final velocity of a freely falling object. Part (ii) applies the work-energy theorem, where the work done by the resistive force of the sand equals the initial potential energy of the coconut, as all its energy is used to create the depression.