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?
The balloon has fallen 60.4 meters.
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
Rearrange that equation to solve for
#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")#