Problem — Speed of a falling stone

From height to impact speed. A stone falls from $h = 10\;\mathrm{m}$ in a vacuum. Calculate the speed at which it hits the ground.

Solution

Data: $h = 10\;\mathrm{m}$, fall in a vacuum (no air resistance), starting from rest.

Conservation of mechanical energy. The initial potential energy becomes entirely kinetic on arrival:

$mgh = \tfrac{1}{2}mv^2 \quad\Rightarrow\quad v = \sqrt{2gh} = \sqrt{2\cdot 9{,}81\cdot 10} = \sqrt{196{,}2} \approx 14{,}0\;\mathrm{m/s}$

$\ev{v \approx 14{,}0\;\mathrm{m/s} \approx 50\;\mathrm{km/h}}$

Physical reading. The mass does not appear: any stone, light or heavy, reaches the ground at $14\;\mathrm{m/s}$ (in a vacuum). Converting, $14{,}0\cdot 3{,}6 \approx 50\;\mathrm{km/h}$: falling from $10\;\mathrm{m}$ (third floor) is equivalent to being hit at urban speed.

Collegamenti

Argomenti: Work and energy Concetti: Conservation of mechanical energy · Gravitational potential energy Competenze: Conservation of energy