Which Object Travels Further: Mass or Velocity?

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When two objects of different masses are propelled upwards at the same velocity, the distance they travel is primarily influenced by gravitational forces rather than mass. In a vacuum, both objects would reach the same height due to gravity acting equally on them, regardless of their mass. However, in the presence of air resistance, the object with less mass may experience a greater deceleration, potentially affecting its ascent. The discussion invites consideration of scenarios with and without air, emphasizing the role of gravity as highlighted by Galileo Galilei. Ultimately, the question revolves around understanding the effects of mass and external forces on motion.
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Hello friends,
When two objects with different mass is propelled with same velocity, straight upwards into air, which object would travel more. The one with less mass or more??

Hope you guys would sure post your comments
 
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Tell us what you think, first. :smile:
 
Mathewsaji said:
Hello friends,
When two objects with different mass is propelled with same velocity, straight upwards into air, which object would travel more. The one with less mass or more??


What do you think and why?
You might try imagining that you have a motion picture of the two masses leaving the ground at the same time and at the same speed and climbing to their peak heights - what would it look like if you played it backwards?
 
And also decide if you want to imagine a scenario where there is air or where there is only gravity. How do you think that would change things, if at all?
 
Hint: Galileo Galilei
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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