Does Instantaneous Velocity Account for Launch Height in Kinematics?

In summary, the conversation is about a student working on a special relativity assignment and trying to understand the relationship between velocity, height, and time for objects dropped from different heights. The moderator clarifies that the formula being used is non-relativistic. The student expresses their stress and difficulties in understanding the material, but the moderator offers support and encourages them to ask questions.
  • #1
starstruck_
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<Moderator's note: Split from another thread and thus no template.>
I am working on my special relativity assignment right now, and it said to find the velocity of an object when it hits the ground. The height the object is launched at is > 0.

Question: comparing that velocity to the instantaneous velocity, does the instantaneous velocity not account for the fact that an object would have a higher velocity at a given point if it’s launched from a greater height?

Say you had two objects whose height can be modeled by the function y(t) = y0+ by-0.5gt^2

When you find the instantaneous velocity, the y0 term disappears. However, we know that the velocity of an object would be greater if it has a greater height.

What’s the difference here?
 
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  • #2
starstruck_ said:
<Moderator's note: Split from another thread and thus no template.>
I am working on my special relativity assignment right now, and it said to find the velocity of an object when it hits the ground. The height the object is launched at is > 0.

Question: comparing that velocity to the instantaneous velocity, does the instantaneous velocity not account for the fact that an object would have a higher velocity at a given point if it’s launched from a greater height?

Say you had two objects whose height can be modeled by the function y(t) = y0+ by-0.5gt^2

When you find the instantaneous velocity, the y0 term disappears. However, we know that the velocity of an object would be greater if it has a greater height.

What’s the difference here?
The question is a bit confused. If I understand correctly, you are considering two objects dropped from a certain initial height and on which only gravity is acting? And you are asking about the instantaneous velocity when they have reached some final height yf, right?

You are right that yo drops out, but the key point is that the time that the will have taken for each object will be different. For the one dropped from a larger height, the time taken to reach the final position yf will be larger. That's why the velocity will be larger for that object.
 
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  • #3
nrqed said:
The question is a bit confused. If I understand correctly, you are considering two objects dropped from a certain initial height and on which only gravity is acting? And you are asking about the instantaneous velocity when they have reached some final height yf, right?

You are right that yo drops out, but the key point is that the time that the will have taken for each object will be different. For the one dropped from a larger height, the time taken to reach the final position yf will be larger. That's why the velocity will be larger for that object.

Thank you! That’s what I reasoned out before I confused my self.

This assignment just has me stressed out, I didn’t learn anything in this class, it’s so hard to follow what he’s doing and now I have to do dimensionless analysis all of a sudden. Oof
 
  • #4
starstruck_ said:
Thank you! That’s what I reasoned out before I confused my self.

This assignment just has me stressed out, I didn’t learn anything in this class, it’s so hard to follow what he’s doing and now I have to do dimensionless analysis all of a sudden. Oof
You are welcome. Although I am a bit puzzled since you mention SR in your title but the formula you use is non relativistic.
 
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  • #5
nrqed said:
You are welcome. Although I am a bit puzzled since you mention SR in your title but the formula you use is non relativistic.

We haven’t started actual SR yet, we’ve been doing dimensionless analysis to go from the Galilean theory to the Newtonian theory over the past 3 weeks (and I absolutely do not understand anything, or at least I didn’t until I worked my way through part of this assignment).

EDIT: it’s just practice with kinematics formulas we already know
 
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  • #6
starstruck_ said:
We haven’t started actual SR yet, we’ve been doing dimensionless analysis to go from the Galilean theory to the Newtonian theory over the past 3 weeks (and I absolutely do not understand anything, or at least I didn’t until I worked my way through part of this assignment).

EDIT: it’s just practice with kinematics formulas we already know
Ah ok, that makes sense now :-) Best luck. And don't hesitate to ask questions here!
 

Related to Does Instantaneous Velocity Account for Launch Height in Kinematics?

1. What is special relativity?

Special relativity is a theory developed by Albert Einstein that describes how objects and events behave in the absence of external forces, such as gravity. It is based on two postulates: the principle of relativity, which states that the laws of physics are the same for all observers in uniform motion, and the constancy of the speed of light, which states that the speed of light in a vacuum is the same for all observers regardless of their relative motion.

2. How does special relativity affect velocity calculations?

Special relativity introduces the concept of time dilation and length contraction, which affect the way we measure velocities in the universe. It also introduces the idea of relative velocities, where the observed velocity of an object can change depending on the observer's frame of reference.

3. How do you calculate velocity in special relativity?

The formula for calculating velocity in special relativity is v = u / √(1 - (u^2/c^2)), where v is the observed velocity, u is the relative velocity, and c is the speed of light. This formula takes into account time dilation and length contraction, and is different from the classical formula of v = d/t.

4. Can an object travel faster than the speed of light in special relativity?

No, according to special relativity, the speed of light is the maximum speed that any object can attain. As an object approaches the speed of light, its mass increases and the amount of energy required to accelerate it increases exponentially, making it impossible to reach or exceed the speed of light.

5. How does special relativity impact our understanding of time and space?

Special relativity challenges our traditional understanding of time and space as absolute concepts. Instead, it suggests that time and space are relative to the observer's frame of reference, and can be affected by factors such as motion and gravity. This has led to the concept of spacetime, where time and space are interconnected and can be described as a four-dimensional continuum.

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