# A man stands on a crane and throws a water balloon down at at 21 m/s. He finds that it takes 2.4s for the balloon to hit the ground. How far has the balloon fallen when it is travelling 40.3 m/s?

Aug 30, 2015

The balloon has fallen 60.4 meters.

#### Explanation:

You know that the ballon was thrown where the man sits with an initial velocity of 21 m/s.

Moreover, you know that it took the balloon 2.4 seconds to hit the ground. To figure out the distance it travelled when its velocity was equal to 40.3 m/s, you need to use the formula

${v}^{2} = {v}_{0}^{2} + 2 \cdot g \cdot h \text{ }$, where

$v$ - the velocity at which you measure the distance, i.e. 40.3 m/s;
${v}_{0}$ - the initial velocity of the balloon;
$h$ - the distance it covered before it reached the velocity $v$;

Rearrange that equation to solve for $h$

$h = \frac{{v}^{2} - {v}_{0}^{2}}{2 \cdot g}$

h = ((40.3""^2 - 21^2)"m"^color(red)(cancel(color(black)(2)))/color(red)(cancel(color(black)("s"^2))))/(2 * 9.8color(red)(cancel(color(black)("m")))/color(red)(cancel(color(black)("s"^2)))) = color(green)("60.4 m")