Answer to Question #217383 in Physics for ran li

Question

Use the information below to answer the following 2 questions.

A 0.80-kg coconut is growing 10 m above the ground in its palm tree. The tree is just at the edge of a cliff that is 15 m tall.

1.The maximum speed of the coconut if it fell to the ground beneath the tree is ___m/s. (Give your answer with the correct number of sig digs and do not include units).

2.The maximum speed of the coconut if it fell from the tree to the bottom of the cliff is ___m/s. (Give your answer with the correct number of sig digs and do not include units).

Answer 1

1. The maximum speed $v$ (the speed just before the collision) is determined by its kinetic energy at this moment. According to the energy conservation law, the final (just before the collision) kinetic energy of an object is equal to its initial potential energy (before the fall starts). Thus, have:

$$\dfrac{mv^2}{2} = mgh\\ v = \sqrt{2gh}$$

where $m$ is the mass of the object, $h = 10m$ is the total vertical distance it travelled, and $g = 9.81m/s^2$ is the gravitational acceleration. Thus, obtain:

$$v = \sqrt{2\cdot 9.81\cdot 10} \approx 14m/s$$

2. In this case everything remains the same, except the initial height. Now it is the distance from the top of the tree to the bottom of the cliff: $h = 10m + 15m = 25m$. Thus, obtain:

$$v = \sqrt{2\cdot 9.81\cdot 25} \approx 22m/s$$

Answer. 1)14, 2) 22.