# Uniformly Accelerated Motion question

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 the maximum height reached.

• Now the book gives me this answer -

• $V_i$ = initial velocity
• $V_f$ = final velocity
• $a$ = acceleration
• $y$ = displacement
• The $V_i$ of the bag when released is the same as balloon at 13 m/s upward

• Choose up as positive
• $y = 0$ at point of release

At highest point, $V_f = 0$. Using the equation $$V_f^2 = V_i^2 + 2a\Delta y,$$ and plugging in the numbers $$0 = (13\,{\rm m/s})^2 + 2(-9.81\,{\rm m/s^2})y,$$ the answer of this equation comes out to $y = 8.6\, \rm m$

The maximum height is 300 + 8.6 = 308.6 m

Now my question is what is the reasoning behind finding the 8.6 meters and adding it to the 300 m? If you dropped the ballast bag from 300 m, wouldn't the maximum height reached by the bag be 300 m?

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. The trajectory of the bag looks like:

in your answer you ignored the initial velocity the bag will rise a little until its velocity is zero then it will fall again , it is like he found the total distance

• This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. – Jim Feb 24 '15 at 18:14
• @JimdalftheGrey: How is this not an answer to the question? – Kyle Kanos Feb 24 '15 at 18:26
• " ignore " can have a different meaning than " insult " which of course i did not mean " insult " the other meaning is "Fail to consider (something significant):" oxforddictionaries.com/definition/english/… – Mohamed Osama Feb 24 '15 at 18:31
• @KyleKanos Okay, it kind of does answer the question. It's just something I see as being more of a comment you'd put on the question than an answer. Perhaps my standards are too strict – Jim Feb 24 '15 at 19:19
• Seems like an answer to me. – David Z Feb 25 '15 at 4:16