Answer to Question #107658 in Mechanics | Relativity for artem

Question

A 0.5 kg water balloon is dropped from a balcony 40 meters from the ground. What is the balloon's velocity just as it hits the ground? (Ignoring air resistance)

Answer 1

Ignoring the air resistance means the case of free fall (gravity is the only force acting upon body).

$h=v_0 t+\frac{gt^2}{2}$

and

$v=v_0+gt$,

where $h$ - height, m; $v$ - velocity, m/s; $v_0$ - initial velocity, m/s; $t$ - time, s; $g$ - acceleration due to gravity, m/s² ($g \approx 9.8 \; m/s^2$). In our case $v_0 =0$, so balloon will hit the ground at

$t= \sqrt{\frac{2h}{g}}$

$v=g \cdot \sqrt{\frac{2h}{g}} = \sqrt{2gh}$

$v=\sqrt{2 \cdot 9.8 \cdot 40} = \sqrt{784} = 28 \; m/s$

Answer: 28 m/s.