Does Instantaneous Velocity Account for Launch Height in Kinematics?

[starstruck_]

<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?

 

[nrqed]

<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.

 

[starstruck_]

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

 

[nrqed]

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.

 

[starstruck_]

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

 

[nrqed]

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!