Help- comparing objects in free fall

[guvava]

Problem: An egg is thrown downwards at 2 m/s from the top of a bridge. At the same moment, a fisherman standing in a stream 30 m beneath the bridge throws a rock upwards at 15 m/s.

How fast will the stone be moving when it and the egg are at the same height above the water?




This is homework from chapters involving the kinematic equations, free fall, and projectile motion



I know I first need to find the distance above the stream at which the rock and egg are at the same place at the same time but I don't know how to do this with the information given and the kinematic equations. I've tried solving using the down direction as positive and up as negative. I can't use displacement=Vi*t+1/2g*t squared for each and set them equal to each other because displacement may not be equal when the two objects meet (this comes out unsolveable when I've tried).

I'm terribly stuck after several hours on this problem. How do I solve it? Thanks!

 

[Shooting Star]

Suppose they meet at a height h from the ground. You can write an eqn for the stone connecting h, its initial velo, and t, which will be h = vs_i - 1/2 gt^2. Similarly for the egg. Now eliminate h and find t. Then use the eqn you've written.

 

[guvava]

It looks like that is what I've already tried to do using h=Vit+1/2gt^2. I keep ending up with 2t=-15t, which doesn't work.

Your equation doesn't include t; isn't that incorrect?

 

[Battlecruiser]

I can't use displacement=Vi*t+1/2g*t squared for each and set them equal to each other because displacement may not be equal when the two objects meet (this comes out unsolveable when I've tried).

You're right. Displacement won't be equal. The height of the egg from the ground is not it's displacement, but rather, 30 minus the distance it has traveled is it's height. You need to take the 30m into account. Then just set those equations equal to each other once you have taken the 30m into account, and you should be able to solve for the time. From there, just plug it into the ($$v_f = v_i + a t$$) equation to solve for the stone's velocity.

By the way, what is the actual answer? When I solved it, I got 3.162 m/s, but I think I screwed up the value of g (If it is negative or positive) when I put it in the equations.

(I've was working on this problem for about 40 minutes, and I couldn't get the answer. I kept getting odd answers like you did, such as negative times. Then I went to go get something to eat and I realized I forgot the 30m when I came back.)

 

[guvava]

By the way, what is the actual answer? When I solved it, I got 3.162 m/s, but I think I screwed up the value of g (If it is negative or positive) when I put it in the equations.

I found time was 1.7 and got 2.25 for the velocity. Thanks! I didn't think about the difference between h and 30.

 

[Shooting Star]

It looks like that is what I've already tried to do using h=Vit+1/2gt^2. I keep ending up with 2t=-15t, which doesn't work.

Your equation doesn't include t; isn't that incorrect?

Which eqn did you mean?