Question

Solve 3a and 3b using energy considerations.
a. 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. What would the
maximum speed of the coconut be if it fell to the ground at the base of the tree?
b. What would the maximum speed be if it fell from the tree to the bottom of the cliff?

Answer 1

Mechanical energy = Potential energy + Kinetic energy. ------------------- ①

Stored potential energy in the coconut at top of the tree = mgh = 0.80 * (10+15) *9.8= 196 j

Now when the coconut falls to the base of the tree, PE at that point = 0.80*9.8*10 = 78.4 j

The lost potential energy has been converted into kinetic energy.
So,

196-78.4 = \(\large\sf \frac{1}{2}mv^2\)

--> 117.6 = 0.4v\(^2\)

-->v = ??


Similarly, when the coconut falls to the base of cliff all the potential energy is lost and has been converted into kinetic energy i.e 196 = \(\large\sf \frac{1}{2}mv^2\). Now calculate the value of v