The dropping of two identical balls without air resistance

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Discussion Overview

The discussion revolves around the behavior of two identical balls dropped from a cliff, with one ball thrown horizontally at 5 m/s and the other at 10 m/s, while ignoring air resistance. Participants explore the implications of these conditions on the time of flight and final speeds of the balls.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions whether both balls will land at the same time and if they will have the same speed upon landing, considering the effects of gravity and horizontal velocity.
  • Another participant notes that both balls have the same initial vertical velocity and acceleration due to gravity, suggesting this may imply they will have the same time of flight.
  • There is a challenge regarding whether the final speeds of the balls can be the same if their initial horizontal speeds differ.
  • A participant emphasizes that the time of flight is determined by vertical motion, while horizontal motion remains constant.
  • One participant acknowledges a mistake in their earlier statement regarding the application of the distance/velocity formula to vertical velocity.

Areas of Agreement / Disagreement

Participants express differing views on whether the final speeds of the balls will be the same, given their different initial horizontal velocities. The discussion remains unresolved regarding the implications of these differences.

Contextual Notes

Participants have not fully explored the relationship between horizontal and vertical components of motion, and there are unresolved questions about how to apply vector addition in this context.

M23
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I was thinking about this and couldn't really figure it out.

You are standing on a cliff and you have two identical balls. In this case, air resistance is to be ignored. The only thing different is that you throw the ball horizontally at different speeds. Let's say you threw ball one at a speed of 5m/s and the other ball at 10m/s

Will the balls land at the same time? Will the balls have the same speed when they land?

My thinking:

Since air resistance is ignored, I know that the horizontal component will be constant throughout. However, I wasn't really sure how no air resistance will affect the behavior of the ball. Could someone please answer the two question above?

Thank you very much.
 
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Some hints..

M23 said:
Will the balls land at the same time?

They have the same vertical velocity at the start.
They have the same vertical acceleration (g).
So will they have the same vertical velocity all the time?
[strike]Time = distance/velocity.[/strike]

Will the balls have the same speed when they land?

Will they have the same vertical velocity?
Will they have the same horizontal velocity?
Do you know how to add vectors?
 
Last edited:
Hi M23 and welcome to PF.

1. No air resistance means that the only force acting on the balls is gravity. In other words, their acceleration is g. What does this imply about the time of flight? You are on the right track.
2. If the balls don't have the same initial speed, why should their final speed be the same?
 
CWatters said:
Time = distance/velocity.
Only in the horizontal direction, of course.
 
Yes sorry not sure why I put that in there when talking about the vertical velocity.
 

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