Beginner problem, but still can not get it.

[Bkr5006]

Water drips from the nozzle of a shower onto the floor 165 cm below. The drops fall at regular (equal) intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall.

a)Find the location of the third drop as measured from the nozzle of the shower when the first drop strikes the floor.
b)Find the location of the second drop as measured from the nozzle of the shower when the first drop strikes the floor.

Thank you for the help.

 

[Doc Al]

Hints: How does distance relate to time for a falling object? How long does it take for a drop to fall from nozzle to floor?

 

[Bkr5006]

Using y=(1/2)at^2
-1.65= .5(-9.8)(t^2)
(-1.65/-4.9)=t^2
sqrt(.34)=t
0.58=time

I figured out the time it took for one droplet to go from the sprinkler head to the ground... then since there was 4 droplets and it said that they were released at equal intervals I divided that by 4 to get .145s separation between them. Next I used the y= (1/2)at^2 forumula again, but this time to find the third droplet I used (.58*.75) to get .435 as my time. Then when I calculated this out I got a distance of .93m, however when I put that as my answer it said it was incorrect. So I'm kinda lost.

 

[berkeman]

Is there a figure that goes with this question? It's ambiguous to me what it is calling the 3rd drop. The rest of the question talks about the 1st drop hitting the floor and the 4th drop just leaving, so I would try calculating the answer for the 3rd drop in order (the one closest to the faucet when the 1st drop hits the floor. Does that answer work? It looks like you are using the correct equations.

 

[Bkr5006]

Nope, there is no figure. The only thing I'm going by the different drops is that they each drop at the same interval, but by the time the 1st drop hits the ground(.58s) the 4th drop is just now leaving the showerhead. So I figured that if I broke that down into 4 equal parts it would work, but I guess it didn't.

 

[berkeman]

Oh, I missed the 4. No, it's 3. The distance from spigot to floor has 3 sections, because only 2 drops are in the air spaced out as the 1st hits the floor.

 

[Bkr5006]

So basically what you're saying is that...

drop 1(coming right out of the head) is at t=0
drop 2(1st drop in air) is at .58/3= t=.19s
drop 3(2nd drop in air) is at .19*2 t=.39s
drop 4(hitting the ground) is at t=.58s

 

[berkeman]

I would have numbered them the other way (like the problem statement initially numbered them), but since the question turns around and says "from the faucet's perspective", your numbering is probably accurate. Do you get the correct answer now?