Where Do Falling and Projected Stones Meet?

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In summary, the problem involves two stones, one falling from a height of 100m and the other projected vertically upwards with a velocity of 25m/s. The goal is to calculate when and where the two stones will meet. Using the equations v2 - u2 = 2as, s = ut + 1/2at2, and v = u + at, the stones will meet when the distance from the ground for both stones is equal, which can also be expressed as the sum of their distances being equal to 100m. Using this information, the answer is calculated to be 4 seconds and a distance of 20m.
  • #1
Yashbhatt
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Homework Statement


This is a very simple question. I even got the answer but I don't exactly I got it. Here it is:
A stone is allowed to fall from the top of a 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where will the two stones meet.


Homework Equations



v2 - u2 = 2as

s = ut + 1/2at2

v = u + at
 
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  • #2
Yashbhatt said:

Homework Statement


This is a very simple question. I even got the answer but I don't exactly I got it. Here it is:
A stone is allowed to fall from the top of a 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where will the two stones meet.

Homework Equations



v2 - u2 = 2as

s = ut + 1/2at2

v = u + at
It will meet when the distance from the ground of two stones become equal.
Calculate that.
 
  • #3
adjacent said:
It will meet when the distance from the ground of two stones become equal.
Calculate that.

We can also say that that they will meet at a point where the sum of distances covered by both the stones will 100. Is that correct?
 
  • #4
Yashbhatt said:
We can also say that that they will meet at a point where the sum of distances covered by both the stones will 100. Is that correct?
No.Do it like this:

How is the distance traveled by the thrown stone determined?
That distance should be equal to the distance between the falling stone and the ground.So it's 100- the distance traveled by the falling stone.

So you should use the equation relating displacement,time,initial velocity and acceleration(g in this case).
 
  • #5
Let A be the point from where the first stone is dropped. Let B be the point from where the second stone is projected. Let the balls meet at P after time t has elapsed. So, then AP + PB = 100. Let v and u be the speeds of the first and second stone respectively. So,
1/2gt2 + ut - 1/2gt2 = 100
So, ut = 100 and we get t = 4s.

Is this correct?
 

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  • #6
It's OK. You can do it this way too.

Actually this shows you that the two stones have a uniform relative motion.
As they both move with the same acceleration, their relative acceleration is zero.
 
  • #7
@nasu Thanks. With this method I got the answer as 4s and distance 20m. Is the answer correct?
 
  • #8
Yashbhatt said:
@nasu Thanks. With this method I got the answer as 4s and distance 20m. Is the answer correct?
It's correct.
My method:
##100-\frac{1}{2}gt^2=25t+\frac{1}{2} \times -gt^2## also gives t=4s s=20m.

EDIT: I just realized that this is the same thing :shy:
 
  • #9
OK . Thanks.
 

Related to Where Do Falling and Projected Stones Meet?

1. What is the significance of the stones meeting?

The stones meeting can hold different meanings depending on the context. In a scientific sense, it could refer to the collision of two celestial bodies or the intersection of geological fault lines. In a spiritual or metaphysical sense, it could symbolize the harmony or balance of energies.

2. How can we predict where the stones will meet?

Predicting where the stones will meet requires extensive research and data analysis. Scientists use various tools and techniques such as mathematical models, satellite imagery, and seismic monitoring to make predictions about the movements and interactions of celestial bodies and geological formations.

3. Is there a specific location where the stones will always meet?

No, there is no specific location where the stones will always meet. The movement and interactions of celestial bodies and geological formations are constantly changing and can be influenced by various factors. Therefore, the location of where the stones will meet may vary over time.

4. What happens when the stones meet?

When the stones meet, it can result in various outcomes depending on the type of stones and the circumstances. For example, when two tectonic plates meet, it can result in earthquakes or volcanic eruptions. When two planets meet, it can result in gravitational interactions or even collisions. The exact outcome can be difficult to predict and can have significant consequences.

5. Can we control where the stones will meet?

No, we cannot control where the stones will meet. The movements and interactions of celestial bodies and geological formations are governed by natural forces and cannot be controlled by humans. However, we can monitor and study these events to better understand and prepare for their potential impacts.

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