Help- comparing objects in free fall

In summary: 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.
  • #1
guvava
3
0
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!
 
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  • #2
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.
 
  • #3
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?
 
  • #4
guvava said:
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 ([tex]v_f = v_i + a t[/tex]) 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.)
 
Last edited:
  • #5
Battlecruiser said:
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.
 
  • #6
guvava said:
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?
 

Related to Help- comparing objects in free fall

1. What is free fall and how does it differ from regular falling?

Free fall is the motion of an object under the influence of gravity only, with no other external forces acting on it. This means that the object is accelerating downwards at a constant rate of 9.8 meters per second squared. Regular falling, on the other hand, may involve external forces such as air resistance or friction, causing the object to fall at varying rates.

2. How do you compare the motion of objects in free fall?

To compare the motion of objects in free fall, you can measure and analyze their acceleration, velocity, and displacement. These variables can be calculated using the equations of motion for free fall, such as a = g (where a is acceleration and g is the acceleration due to gravity), v = gt (where v is velocity and t is time), and d = 1/2 gt^2 (where d is displacement).

3. How does the mass of an object affect its motion in free fall?

In free fall, the mass of an object does not affect its motion. This is because gravity acts equally on all objects regardless of their mass, causing them to accelerate at the same rate. This was famously demonstrated by Galileo Galilei when he dropped objects of different masses from the Leaning Tower of Pisa and observed that they reached the ground at the same time.

4. What is terminal velocity and how does it relate to free fall?

Terminal velocity is the maximum velocity that an object can reach when falling through a fluid, such as air or water. In free fall, an object will continue to accelerate until it reaches its terminal velocity, at which point the upward force of air resistance equals the downward force of gravity, resulting in a net force of zero and a constant velocity.

5. How does the location or environment impact the motion of objects in free fall?

The location or environment can impact the motion of objects in free fall in two ways. First, the acceleration due to gravity may vary slightly depending on the altitude and location on Earth due to factors such as the Earth's rotation and shape. Second, the presence or absence of air resistance can greatly affect the motion of objects in free fall. In a vacuum, with no air resistance, objects will fall at the same rate regardless of their shape or size. However, in the presence of air resistance, objects with larger surface areas will experience greater resistance and fall at slower rates than objects with smaller surface areas.

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