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 [tex]a_{y} = -9.8 m/s^{2}[/tex]
Since the balloon dropped from a given height, its initial velocity [tex]V_{i} = 0[/tex]
Final Velocity [tex]V_{f} = ?[/tex]
Using the equation [tex]V^{2} _{f} = V^{2} _{i} + 2(a_{y} )(h)[/tex]
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.
