Speed of rocks when they hit the ground

In summary, the question is about the speed of two rocks thrown in opposite directions before they hit the ground. The answer is that they should hit the ground at the same speed but at different times. To show this mathematically, one can use the formulas for objects in a gravity field and the conservation of mechanical energy. This relates the initial kinetic energy to the final potential energy.
  • #1
limonade
7
0

Homework Statement



If I throw a rock upwards with an initial velocity and throw a rock downwards, what is the speed of the rocks just before they hit the ground?

Homework Equations





The Attempt at a Solution

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They should hit the ground at the same speed and different times. I would use the conservation of mechanical energy, but someone I'm speaking to disagrees with me that they have same speed.

How would you show this mathematically?
 
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  • #2
Use the formulas for objects traveling in a gravity field. You are studying physics, I presume.
 
  • #3
See your initial kinetic energy is the final potential energy.
use this relation.
 

1. What is the speed of rocks when they hit the ground?

The speed of rocks when they hit the ground can vary greatly depending on a number of factors, such as the height from which they are dropped, the shape and size of the rock, and the air resistance. In general, rocks will accelerate towards the ground at a rate of approximately 9.8 meters per second squared due to gravity.

2. Can the speed of rocks when they hit the ground be calculated?

Yes, the speed of rocks when they hit the ground can be calculated using the equation v = √(2gh), where v is the final velocity, g is the acceleration due to gravity, and h is the height from which the rock is dropped. However, this calculation may not be entirely accurate as it does not take into account factors such as air resistance.

3. How does the shape and size of a rock affect its speed when it hits the ground?

The shape and size of a rock can greatly affect its speed when it hits the ground. Objects with a larger surface area, such as flat rocks, will experience more air resistance and therefore have a lower final speed compared to smaller, more streamlined rocks. Similarly, objects with a larger mass will also experience more gravitational force and therefore accelerate faster towards the ground.

4. Does air resistance play a significant role in the speed of rocks when they hit the ground?

Yes, air resistance can have a significant impact on the speed of rocks when they hit the ground. As mentioned before, objects with a larger surface area will experience more air resistance and therefore have a lower final speed. Additionally, the density of the air and the shape of the object can also affect the amount of air resistance experienced.

5. Is the speed of rocks when they hit the ground the same regardless of the surface they land on?

No, the speed of rocks when they hit the ground can vary depending on the surface they land on. For example, a rock dropped onto a hard, flat surface like concrete will experience a greater impact and come to a stop faster compared to a rock dropped onto a soft, uneven surface like sand. This is due to the different levels of resistance and friction between the rock and the surface it lands on.

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