An apple falls from a tree branch and hits the ground at 8m/s. How tall is the tree?

Question

Please show work, of how you found the mechanical energy.

Answer 1

From the principle of conservation of energy, the sum of potential energy (E_p) and kinetic energy (E_k) must remain constant.

Since the apple falls from a branch it was at rest just before starting falling: therefore it has only potential energy given by E_p = mgh and zero kinetic energy. The total energy is therefore mgh.

When the apple hits the ground all potential energy has been converted into kinetic energy E_k =(1/2)mv² and the potential energy at the ground level is zero. The total energy is therefore (1/2)mv²

We therefore impose that the initial total energy (only potential) is equal to the final total energy (only kinetic)

mgh=(1/2)mv²

which implies

h=v²/g.

In your case you have h=64/9.81 m= 6.52 m

Best,

Davide