Question

An apple falls from a tree and hits the ground 13.4 m below. With what speed will it hit the ground? The acceleration of gravity is 9.8m/s

Answer 1

When the apple is above the ground at height $H$ with no speed, it has total energy equal to just potential energy: $E_1 = U_1 = m g H$. Just when it hits the ground, it has some speed $v$, and zero potential energy, hence the total energy is $E_2 = T_2 = \frac{m v^2}{2}$ . By the law of conservation of energy, $E_1 = E_2$, from where $v = \sqrt{m g H} \approx 16.21 \frac{m}{s}$,