Proof of Projectile Motion: Displacement and Gravity Explained

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Discussion Overview

The discussion revolves around the proof of projectile motion, specifically examining the relationship between displacement, horizontal speed, and the effects of gravity on a body thrown horizontally from a cliff. Participants explore the implications of gravity on the time of flight and horizontal displacement.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why gravity is not considered in the calculation of displacement when a body is thrown horizontally, suggesting that displacement equals horizontal speed times time.
  • Another participant argues that gravity must be considered, as it affects the vertical motion and determines how quickly the body reaches the ground, influencing the horizontal distance traveled.
  • There is a challenge regarding whether the formula for range (horizontal speed times time) is valid, with emphasis on the role of gravity in determining the time of flight.
  • A participant emphasizes that while gravity does not affect horizontal motion, it is crucial for determining the time taken for the object to fall, which in turn affects horizontal displacement.
  • A later reply acknowledges the clarification regarding the impact of gravity on time, indicating a shift in understanding.

Areas of Agreement / Disagreement

Participants express differing views on the role of gravity in calculating displacement and time. While some recognize the necessity of considering gravity in the context of projectile motion, others initially question its relevance, leading to an unresolved debate over the implications of these factors.

Contextual Notes

The discussion highlights the dependence on the definitions of displacement and the assumptions regarding the independence of horizontal and vertical motions in projectile motion. There are unresolved aspects regarding the precise relationship between horizontal speed, time, and the effects of gravity.

Jadaav
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A body is thrown horizontally from a cliff with an initial horizontal speed. It hits the ground at a distance X from its initial position. It is said that the displacement = horizontal speed * time.

When the body falls, gravity acts upon it. So why don't we consider gravity ?

Any proof that the displacement would be the same as above if the same body would have moved with the same initial speed on a flat horizontal path for the same time period ?

Of course in the 2nd situation, it would continue to move infinitely.
 
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Jadaav said:
When the body falls, gravity acts upon it. So why don't we consider gravity ?
Of course you must consider gravity. The vertical motion under gravity determines how quickly the body reaches the ground and thus how far it's able to get horizontally before it lands.
 
Then range = horizontal speed * time is false ?
 
Jadaav said:
Then range = horizontal speed * time is false ?

What determines the "time"? It is the fall of the object due to gravity!

While gravity doesn't affect the motion in the horizontal direction, it affects the time taken for the object to move! That is how gravity comes in!

You should go back and resolve this problem, and pay attention to what factors determine the time of motion that you used for the horizontal component.

Zz.
 
Ok thanks for clearing my doubt on the subject. I didn't give much thought on the time which is already affected by gravity.
 

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