A ballast bag is dropped from a balloon that is 300 m above the ground and rising at 13 m/s. For the bag, find (a) the maximum height reached, (b) its position and velocity 5.0 s after it is released, and (c) the time at which it hits the ground.
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If you start with the bag stationary at 300m then drop it the bag is going to fall straight down, and its maximum height would indeed just the 300m point it started from.
However you're not starting with the bag stationary. You're starting with the bag moving upwards at 13 m/s. So the bag is going to start at 300m then move up, come to a halt, then start falling down again. That means the top of its trajectory is above 300m.
The 8.6m you've calculated is the distance an object moves upwards if it starts with an initial upwards velocity of 13 m/sec.
Explanation:
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