# Kinematics - When do they meet?

Sean1218

## Homework Statement

A stone is dropped off a cliff of height h. At the same time, a second stone is throne straight upward from the base of a cliff with an initial velocity v. Assuming that the second rock is thrown hard enough at what time t will the two stones meet.

## Homework Equations

Uniform acceleration equations

## The Attempt at a Solution

I tried a few different things, and nothing worked. I don't have anything written down right now though.

I just wrote Δd = v1Δt + 1/2gΔt2, for both stones, substituting Δd for x in one of the equations, and h - x in the other.

So, I just had x = 1/2gΔt2 and h - x = v1Δt + 1/2gΔt2

I tried combining them, but I got to a point where I didn't think I could do anything else with it, and it just felt wrong.

Am I thinking about it wrong?

Last edited:

## Answers and Replies

jrab
if you told me the numbers i could solve it for you :p

Sean1218
if you told me the numbers i could solve it for you :p

There are no numbers, could you explain how to solve it?

jrab
let me get some paper i gtg eat so ill tell you when i find out

Homework Helper
Hi Sean! I just wrote Δd = v1Δt + gΔt2, for both stones, substituting Δd for x in one of the equations, and h - x in the other.

So, I just had x = gΔt2 and h - x = v1Δt + gΔt2

Yes, you have the correct basic idea, but

i] it's 1/2 g∆t2, isn't it?

ii] shouldn't one of those gs be minus?

(btw, you'll notice something unexpectedly disappears … why do you think that is?)

(and jrab, on this forum you mustn't give answers, you must only help)

Sean1218
ah haha, forgot the 1/2. That doesn't really change my result much though.

I still end up with 0 = gΔt2 + v1Δt - h, and I don't see how I can use the quadratic formula without numbers. Nothing disappeared or cancelled out from what I can tell, since moving the - 1/2gΔt2 to the other side just makes it positive. And why would one of the g's be negative? I'm using v1 for both, so the equation is just + g.

Homework Helper
But isn't your v1 up, and your g down?

Sean1218
Not really sure what you mean. v1 is going up, and g is down, but I can't just include negatives can I? g = -9.8, if I made g negative, at the end I'd just get a positive acceleration, but g isn't positive. g is the same for both equations, v1 = 0 for the first one, and it's positive for the second stone, but I don't see how I can declare that it'll always be positive without plugging in numbers, if you know what I mean.

Homework Helper
Oh i see, you're using g = minus 9.8 (we don't usually do that) …

ok, but then if your x is always positive, doesn't the first g need to have a minus?

Anyway, here's another approach … what is the relative acceleration of the two stones? Sean1218
The first equation is the same as the second equation though. v1 is 0 so the first term is 0, but g is still g (-9.8 if you plug it in) as far as I know.

and I wouldn't know where to start with relative acceleration

Homework Helper
… I wouldn't know where to start with relative acceleration

Well, what is the acceleration of the first stone, and what is the acceleration of the second stone?

Sean1218
it's the same for both, accel due to gravity.

Homework Helper
So the relative acceleration is … ? Sean1218
relative to each other, 2g I guess

Homework Helper
Nooo! it's zero, isn't it?

And if the relative acceleration is zero, then the relationship between relative distance relative time and relative speed is … ? I'm off to bed now :zzz: …

Sean1218
Can anyone else help with the original method I was using (after adding in the 1/2 that is)?

Sean1218
Anyone?

The legend
an easier way would be relative motion as tiny-tim suggested.
And accordingly you can plug in the equations of motion considering the relative acceleration as 0.
rel(d) = rel(speed) * time.

easy as that.

The legend
So, I just had x = 1/2gΔt2 and h - x = v1Δt + 1/2gΔt2

Using g=+9.8m/s^2
The second one in there would have a= -g.

Now add them up, eliminating few stuff you can get your answer, your way.

Sean1218
Using g=+9.8m/s^2
The second one in there would have a= -g.

Now add them up, eliminating few stuff you can get your answer, your way.

Alright, thanks! So, why would one of them be -g instead of g? Accel due to gravity is always negative, so I don't really see why.

The legend
we dont usually use g to be negative, the direction decides what g is. Only the thing is g acts downwards, and if you choose up to be positive g becomes negative and if you choose down to be positive g becomes positive.

So get it?

Sean1218
Not really, I was working through it assuming up is positive, and down is negative, for both equations. Was there something I did that indicated otherwise?

The legend
then in your first equation x would be negative....