Projectile Motion: Solving for Meeting Point of Projectile and Falling Object

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Homework Help Overview

The discussion centers around a mathematical proof regarding the meeting point of a projectile and a falling object, exploring the principles of projectile motion and gravitational effects. Participants are examining the conditions under which these two objects will intersect, regardless of their initial speeds or distances involved.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to articulate the relationship between the projectile's horizontal motion and the vertical fall of the object. Questions arise about how to mathematically demonstrate that both objects will meet, with some suggesting the use of graphs to illustrate the vertical and horizontal components of motion.

Discussion Status

The discussion is ongoing, with participants sharing insights and exploring different frames of reference. Some guidance has been offered regarding the relationship between time, distance, and velocity, but no consensus has been reached on a definitive mathematical approach.

Contextual Notes

Participants are working within the constraints of a homework assignment that requires a mathematical proof, and there is an acknowledgment of the need to clarify assumptions about the initial conditions of the projectile and the falling object.

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Homework Statement



Prove mathematically that regardless of the range and initial speed, a projectile and a falling object will always meet.

Homework Equations



Vf^2 = Vi^2 + 2ad, d = vi t + 1/2 at^2, d = vt.. etc basic constant velocity and acceleration formulas.

The Attempt at a Solution



this question followed one with specific information given (which I was able to easily solve) and I know how to explain the answer in words; a projectile is under the same force of gravity as th e falling object, so after a certain amount of time the horizontal component of speed will meet up with the falling object, obviously if there is less distance and/or a higher horizontal speed this will occur quicker, but how do I show this conclusion using mathematical formulas?
 
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If you are in the frame of reference of the falling object, and it is aimed at you and is fired at the moment you drop, then it will strike you straight away, because you and the projectile are moving together. From your point of view it will be traveling straight at you the whole way.
 
LowlyPion said:
If you are in the frame of reference of the falling object, and it is aimed at you and is fired at the moment you drop, then it will strike you straight away, because you and the projectile are moving together. From your point of view it will be traveling straight at you the whole way.

I understand the concept in words but I can't come up with a mathematical equation to prove it. Do I just draw a graph to show that the vertical components are the same and that the amount of times it takes to reach the object is just the horizontal component calculated via d = vt?
 
You can note that in the accelerating frame of reference of the object/projectile world there is no net acceleration on either relative to the other.

You know the time to fall is given by Height = 1/2*g*t2
And the distance is D

So long as the projectile has a V greater than the D/t then it should strike before the ground intervenes to interrupt things.
 

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