Question

the speed of a ball is 2.0 m/s as it falls past a window of a tall building. How fast, in m/s, is it going as it passes another window 3.0 m below?

Answer 1

Law of conservation of energy says:

$$E = const$$

So,

$$E_{k0} + E_{p0} = E_{k1} + E_{p1}$$ $$E_k - \text{kinetic energy}, E_p - \text{potential energy}$$ $$\frac{m v_0^2}{2} + m g h = \frac{m v^2}{2} + 0$$

It's easy to receive:

$$v = \sqrt{v_0^2 + 2 g h}$$

So,

$$v = \sqrt{2^2 + 2 * 10 * 3} = 8 \left(\frac{m}{s}\right)$$