How Do You Calculate the Position of Two Falling Stones with a Time Delay?

[scavok]

I didn't have much trouble with the 1-D 1 object kinematics, but I'm having a lot of trouble with 2 objects. I'd just like some help setting the problem up:

Two stones are dropped from the edge of a 60m cliff, the second stone 1.6s after the first. How far below the top of the cliff is the second stone when the separation between the two stones is 36m?
I thought the best way to set this up would be:

X = Displacement of first stone in terms of a
Y = Displacement of second stone in terms of a
X-Y=36m
(vt+.5at²)-(vt+.5at²)=36

(Pretend I have subscripts to indicate they aren't the same variables and don't cancel each other out right away.)

I don't know if that's right, and even if it is, I just can't think of how to factor in the 1.6s.

A little guidance on how to get started would be appreciated.

 

[frozen7]

X = Displacement of first stone
Y = Displacement of second stone
X-Y=36m
(vt+.5at2)-(vt+.5at2)=36

the initial speed is zero for each stone, and the acceleration is same for both also since it is free fall, so the only variables is time.
I solve it by:

taking time taken by first stones = time taken by second stones + 1.6

I think the problem can be solved by using this assumption.

 

[scavok]

I still can't get it. The correct answer should be 10.9m.

The initial speed is zero, and a=g so the equation should look like this:
(.5gt²)-(.5gt²)=36m

Where does the +1.6s come in?

(.5gt²)-(.5g(t+1.6s)²)=36m?

vv Very cool, thank you.

 

[HallsofIvy]

You need to be more precise! Let's say that the distance the first stone is below the cliff is x₁ and the distance the second stone is below the cliff is x₂. Let t₁ be the time the first stone has been falling and t₂ the time the second stone has been falling. (No, I will not "pretend you have subscripts- put them in!).

Another problem is that you have as formula (1/2)gt²+ vt but, as frozen7 said, the initial velocityis 0:
x₁= (1/2)gt₁² and
x₂= (1/2)gt₂². The distance between them is x₁1- x₂= (1/2)gt₁²-(1/2)gt₂².

Now, what is the relationship between t₁ and t₂? You appear to be replacing what I have called t₂ with t₁+ 1.8. Can't you see that that can't be right? The second stone doesn't start falling until 1.8 s after the first. The second stone is falling for less time than the first, not more! t₂ must be less than t₁. You have t₂= t₁- 1.8. You can replace t₂ by t₁- 1.8, solve for t₁ and then find x₂ or replace t₁ by t₂+ 1.8, solve for t₂ and use that to find x₂. The second way might be simpler since it is x₂ you want to find.