You are trying to find out how high you have to pitch a water balloon in order for it to burst when it hits the ground. you discover that the balloon bursts when you have pitched it to a height of 10 m. with what velocity did the ballon hit the ground? the acceleration of gravity is 9.8 m/s^2. the positive direction is up, to the velocity when it hits is negative. an

It is given that the balloon fell from a height of 10 m.

So, its displacement in the vertical direction h = -10 m, because the question specifically asks us to take the upward direction as +.

Acceleration in the vertical direction  

Since the balloon dropped from a given height, its initial velocity

Final Velocity

Using the equation  

and plugging in the known values, we get  [tex]V^{2} _{f} = 0 + 2(- 9.8)(- 10)

Solving this for  [tex]V_{f}, we get [tex]V_{f} = 14 m/s or [tex]V_{f} = -14 m/s

Since the question is asking us for the final velocity, which faces downward direction, we choose [tex]V_{f} = -14m/s as the final answer.

what is the actual question though?