Where did the water balloon fall?

[Medgirl314]

Homework Statement

A boy is on top of a 12 m tall building. He throws a water balloon horizontally, releasing it at a height of 1 m above the top of the building. The water balloon is thrown at 30 mi/h and is aimed at the balconies of an apartment building across the street, 18 m away horizontally. If each story of the apartment building is 3 m high, which balcony gets hit by the water balloon, 1st, 2nd,3rd or 4th floor?

Homework Equations

t=x/v
y=y0+v0t1/2 a(t^2)

The Attempt at a Solution

I attempted to convert the mi/h to m/s and got 80.3 m/s. I used t=x/v to get my time:

t=x/v
t=18/80.3
t=0.22 s

The time seems reasonable enough.

Then I tried using y=y0+v0t+1/2 a(t^2) to find how far down the balloon fell.

y=y0+v0t+1/2a(t^2)
1/2 a(t^2)
y=0+0+1/2 a(t^2)
y=1/2a(t^2)
y=1/2(9.8)(0.22^2)
y=1/2(9.8)(0.0484)
y=0.24 m

Something seems off, but I can't place it. If this answer is right, does that mean it will land on the 4th(top) floor of the building?

Thanks!

 

[SteamKing]

Try your conversion of 30 mi/hr to m/s again. 80.3 m/s is a very fast clip.

 

[Medgirl314]

Hm, I thought so. 30 mi=48280.3 m. OH, I see. I calculated to m/min. I need to divide by 60 again, correct? So 1.3 m/s.

 

[SteamKing]

1.3 m/s is a casual strolling speed. You need to set up your calculations in an organized fashion and not try to 'shoot from the hip'. It's not clear where 80.3 m/s came from originally.

 

[Medgirl314]

I didn't think about it that way. Hmm. Okay, so 30 mi/h=48280.3 m/h. Line up the unit conversion so that the hours cancel out. 48280/3600 s=13 m/s. That seems right, finally.

 

[Medgirl314]

Is the time right?

 

[Medgirl314]

I'm getting 9.3 meters, which would put it at the second (next to bottom) floor. Feel free to confirm or correct the answer! :)

 

[lightgrav]

13.4 m/s hits in 1.34s after dropping 8.8m (from 13m start).
avoid round-offs (especially for things that get squared, like t here), by using the value in the calculator display register.

 

[Medgirl314]

Ah, I see. I used 1.38 seconds. Now I'm getting 8.8 as well. So this should put the balloon at the third (from bottom) floor, correct?

Thanks again!

 

[Medgirl314]

This post is only here because I couldn't delete it.

 

[lightgrav]

huh? 13m - 8.8m = ? 1st floor 0 to 3m, 2nd floor 3m to 6m, 3rd floor 6m to 9m, 4th floor 9m to 12m ... right?

 

[Medgirl314]

4.2 m. Correct, I don't think I'm thinking about the diagram correctly. It would actually be the second floor, right?