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?

1 Answer
Stefan V.
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 * g * h" "#, 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 = (v^2 - v_0^2)/(2 * 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")#

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