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Old Sep 27th 2010, 03:49 PM   #1
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Having trouble with this...

Hi, Stuck on this one, I have a drawing but it does not make sense.
Is this 1D or 2D kinematics??

a hot air balloon is rising straight up with a speed of 3.0 m/s. A ballast bag is released from rest relative to the balloon when it is 9.5 m above the ground.

How much time elapses before the ballast bag hits the ground.
So I have Vo = 0 m/s as it's from rest relative to the balloon?? is that correct.
a = -9.8 m/ss
d = 9.5 m

Do I use d = Vot + 1/2 at^2. And if so how to do I get the 2 t's into 1. I tried to re arrange and it's not working out.

Please help me start this please, thanks. Tell me if I am on the right track.
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Old Sep 27th 2010, 05:03 PM   #2
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I was told -3.0 m/s and the a=9.81, as it's relative to the air, not ground, so the frame of reference is different.

The answer is 1.7 s.
Not getting it, what did you do?
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Old Sep 27th 2010, 05:09 PM   #3
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Let me have a go.

Vo = -3.0
a = 9.81
d=9.5

d = Vot + 1/2 at^2

9.5 = -3t + 1/2 (9.81 t^2)

4.905 t^2 - 3 t - 9.5 = 0 with some quick rearranging. There are numerical methods to solve this, but because it's so horrible, I had my calculator speed through it.


t = 1.73 or t = -1.12

As t cannot be negative, we discard the t = -1.12, so t=1.73

Is this correct?

Last edited by Quacky; Sep 27th 2010 at 05:11 PM.
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Old Sep 27th 2010, 06:03 PM   #4
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I know there is the quadratic way of solving for t, but my teacher said there would be no questions like that on tests, using the quad function.

How would you key that into your calculator otherwise, or type out the formula on how you did it.

That is always a tough one to figure out.
Thanks
AND yes you got the answer.
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Old Sep 28th 2010, 04:06 PM   #5
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Vo = -3.0
a = 9.81
d=9.5

There is another way, which is probably easier to follow:

Using v^2 = Vo^2 + 2ad

We get:

v^2 = 9 + 2 x 9.81 x 9.5
So v^2= 192.39
v = 13.87

Now using V = Vo + at
13.87 = -3 + 9.81t
Simple rearranging will give:
16.87 = 9.81t
t= 16.87/9.81 = 1.72

This may be easier than using the quadratic formula, which is icky with such horrible decimals.

I've induced a slight margin of error here because I rounded my answer for v, but as long as you use a suitable degree of accuracy, it should work out fine.

Last edited by Quacky; Sep 28th 2010 at 04:11 PM.
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