Solve Dropped Samovar Problem w/ Physics HW

[icurryx3]

Homework Statement

A Russian balloonist floating at an altitude of 120 meters accidentally drops his samovar and starts to ascend at the constant speed of 1.5 m/s. How high will the balloon be when the samovar reaches the ground?

Homework Equations

D = V0T + 1/2(A)(t)^2
V = V0 + AT
V^2 = V0^2 + 2ad

The Attempt at a Solution

I tried to use V0, V, A, D, T, to set up the problem but I'm not quite sure which variable fits where.

 

[HallsofIvy]

For the falling samovar, V0 is 0, and A is -9.8 m/s^2. It will "hit the ground" when D= -120 since you are taking D= 0 at 120 ft.
Put those numbers into your equation and solve for t.

For the balloon, V0 is 3/2= 1.5 m/s and A is 0. Find D when t is the value you got above. Don't forget to add 120 ft to get the actual height above the ground.

 

[SteamKing]

Homework Statement

A Russian balloonist floating at an altitude of 120 meters accidentally drops his samovar and starts to ascend at the constant speed of 1.5 m/s. How high will the balloon be when the samovar reaches the ground?

Homework Equations

D = V0T + 1/2(A)(t)^2
V = V0 + AT
V^2 = V0^2 + 2ad

The Attempt at a Solution

I tried to use V0, V, A, D, T, to set up the problem but I'm not quite sure which variable fits where.

You've got two independent things going on simultaneously:
1. The samovar falls out of the balloon.
2. The balloon starts rising at constant velocity, after the samovar falls out.

You want to find the altitude of the balloon when the samovar hits the ground.

Start by asking:

1. How long does it take the samovar to fall 120 meters?

 

[icurryx3]

You've got two independent things going on simultaneously:
1. The samovar falls out of the balloon.
2. The balloon starts rising at constant velocity, after the samovar falls out.

You want to find the altitude of the balloon when the samovar hits the ground.

Start by asking:

1. How long does it take the samovar to fall 120 meters?

To find that, I would need to find other key facts about the problem. How can I go about doing this?

 

[SteamKing]

To find that, I would need to find other key facts about the problem. How can I go about doing this?

What key facts are you missing? I thought the problem statement gave sufficient information to find a solution.

 

[icurryx3]

What key facts are you missing? I thought the problem statement gave sufficient information to find a solution.

That's the problem..
I'm having trouble putting the given factors into V0, V, A, D, T.
For instance:
V0=
V=1.5m/s^2
A=-9.81m/s^2
D=120m
T=

 

[icurryx3]

Would this be correct or am I doing it incorrectly?

 

[SteamKing]

Would this be correct or am I doing it incorrectly?

That's the problem..
I'm having trouble putting the given factors into V0, V, A, D, T.
For instance:
V0=
V=1.5m/s^2
A=-9.81m/s^2
D=120m
T=

You didn't read what I wrote in Post #3.

The samovar is falling to the ground independently of what the balloon is doing. Calculate how long it takes the samovar to fall 120 meters.

Remember, the balloon doesn't start to rise until after the samovar falls. So what is the initial velocity of the samovar at the start of its fall?

 

[icurryx3]

You didn't read what I wrote in Post #3.

The samovar is falling to the ground independently of what the balloon is doing. Calculate how long it takes the samovar to fall 120 meters.

Remember, the balloon doesn't start to rise until after the samovar falls. So what is the initial velocity of the samovar at the start of its fall?

Ah, so the set-up would be:
V0=0
V=
A=-9.81m/s^2
D=120m
T=?
I think it would be -120m since the displacement of the samovar changed negatively with the downfall, am I correct? And using this would help me solve for the time?

 

[SteamKing]

Ah, so the set-up would be:
V0=0
V=
A=-9.81m/s^2
D=120m
T=?
I think it would be -120m since the displacement of the samovar changed negatively with the downfall, am I correct? And using this would help me solve for the time?

Yes, with the proper SUVAT formula.

 

[icurryx3]

Yes, with the proper SUVAT formula.

So now, I have the following information for the drop:
V0=0
V=-48.5m/s
A=-9.81m/s^2
D=-120m
T=4.9s
What should my next step be?

 

[SteamKing]

So now, I have the following information for the drop:
V0=0
V=-48.5m/s
A=-9.81m/s^2
D=-120m
T=4.9s
What should my next step be?

Now that you know the time it takes the samovar to fall, how about reading the problem statement again and see if you can complete the solution?

 

[icurryx3]

Now that you know the time it takes the samovar to fall, how about reading the problem statement again and see if you can complete the solution?

For some reason, I am getting the wrong answer..
Here is what I set-up for the height:
V0=1.5m/s
V=
A=-9.81m/s^2
D=?
T=4.9s

 

[icurryx3]

For the falling samovar, V0 is 0, and A is -9.8 m/s^2. It will "hit the ground" when D= -120 since you are taking D= 0 at 120 ft.
Put those numbers into your equation and solve for t.

For the balloon, V0 is 3/2= 1.5 m/s and A is 0. Find D when t is the value you got above. Don't forget to add 120 ft to get the actual height above the ground.

Why is A = 0? Isn't gravity acting down on the balloon?

 

[SteamKing]

Why is A = 0? Isn't gravity acting down on the balloon?

The balloon isn't falling; it's a balloon! Balloons float in the air because they have a lower average density than the air displaced by the balloon.

When the samovar falls out, the balloon suddenly gets lighter and starts to rise, as astounding as that may seem.

 

[icurryx3]

The balloon isn't falling; it's a balloon! Balloons float in the air because they have a lower average density than the air displaced by the balloon.

When the samovar falls out, the balloon suddenly gets lighter and starts to rise, as astounding as that may seem.

Alright but I don't seem to be getting the correct answer despite the V0vadt.
Have I done a mistake?

 

[SteamKing]

Homework Statement

A Russian balloonist floating at an altitude of 120 meters accidentally drops his samovar and starts to ascend at the constant speed of 1.5 m/s. How high will the balloon be when the samovar reaches the ground?

An important part of solving any problem is reading the problem statement carefully.

Alright but I don't seem to be getting the correct answer despite the V0vadt.
Have I done a mistake?

What's V0vadt? Show your calculations.

 

[icurryx3]

I was taught V0VADT which corresponds to your SUVAT formula.
As of now, my formula is the following:
Vo=1.5m/s
V=
A=0
D=?
T=4.9s

 

[SteamKing]

I was taught V0VADT which corresponds to your SUVAT formula.
As of now, my formula is the following:
Vo=1.5m/s
V=
A=0
D=?
T=4.9s

That's not a formula. It's a list of numbers, incomplete.

If the balloon rises at 1.5 m/s for 4.9 s, how far does it rise?

The questions don't get any easier than this, except the one which asks you to write your name on the paper.

 

[icurryx3]

That's not a formula. It's a list of numbers, incomplete.

If the balloon rises at 1.5 m/s for 4.9 s, how far does it rise?

The questions don't get any easier than this, except the one which asks you to write your name on the paper.

Alright so for that, I'll use d=vt.
So the balloon rises 7.35m and if I were to add that to 120m, it would give me 127.35m however, the answer given to me by the teacher indicates that it should be 128m. The thing is, I got 127.35m a while ago but just because it was not exactly 128m, I kept repeating my steps.

 

[SteamKing]

Alright so for that, I'll use d=vt.
So the balloon rises 7.35m and if I were to add that to 120m, it would give me 127.35m however, the answer given to me by the teacher indicates that it should be 128m. The thing is, I got 127.35m a while ago but just because it was not exactly 128m, I kept repeating my steps.

Round-off in an extended calculation can get tricky to handle. For instance, in calculating the falling time of the samovar, did you get 4.9 seconds exactly, or were there more decimal places?

As far as 128 m is concerned, that could be anything from 127.50 m to 128.49 m.

Some things you'll have to let your teachers decide; that's part of their job. Just make sure that your calculations are laid out in an orderly fashion for him or her to review.

 

[icurryx3]

Round-off in an extended calculation can get tricky to handle. For instance, in calculating the falling time of the samovar, did you get 4.9 seconds exactly, or were there more decimal places?

As far as 128 m is concerned, that could be anything from 127.50 m to 128.49 m.

Some things you'll have to let your teachers decide; that's part of their job. Just make sure that your calculations are laid out in an orderly fashion for him or her to review.

Alright. And I probably rounded the 4.9 seconds like you stated.
Thank you for the help!