Kinematics -- Projectile motion problem

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Homework Help Overview

The discussion revolves around a kinematics problem involving projectile motion, specifically focusing on two bullets fired from two guns positioned 10 meters above the ground. Participants are tasked with determining which gun fired first, as well as the displacement and time at which the bullets collide.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss vertical and horizontal displacements and question the assumptions regarding firing velocities and angles. There are attempts to relate time intervals and displacements, with some participants expressing uncertainty about the initial conditions and the relevance of the height given.

Discussion Status

The discussion is active, with participants exploring various interpretations of the problem. Some have offered insights into the assumptions needed for a solution, while others have raised questions about the initial conditions and the implications of different firing angles. There is no explicit consensus on the approach to take, but several productive lines of reasoning are being examined.

Contextual Notes

Participants note the lack of specifications regarding initial velocities and the timing of the shots, which complicates the problem. The modification of the question by the teacher introducing a specific velocity is also mentioned, indicating a shift in the parameters under consideration.

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Poster has been reminded to use the HH Template and show their work toward a solution
One bullet was fired from Gun A and Gun B each at varying time interval. Both the guns are 10 meters above the ground. Calculate: a) Which gun was fired first. b) Displacement and time at which the two bullets will collide.
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What have you done so far? Just the vertical displacement? Or, both vertical and horizontal displacements?
 
First off, you did not use the template. Please do.
Secondly, you have not shown your efforts yet.
Lastly, you should be able to answer at least part a based on your intuition. I guess the assumption is that the firing velocity of both guns is equal.
 
Oh, sorry.
If we consider time as 'T' then by traditionally solving, I got Ta = 1/2Tb. I don't know what to do further. The final answer is 1 second.
And the displacements, I got Sy for A=Sy for B.
 
1 second for Ta or Tb?
I am guessing that trajectory a starts completely horizontal, and b is at 60 degree elevation from horizontal.

Next, you should relate the y displacement positions at the final time:
## v\frac{\sqrt{3}}{2}T_f - \frac{9.8}{2}(T_f)^2 = - \frac{9.8}{2}\left(\frac{T_f}{2}\right)^2##

I don't immediately see how you can find a solution without some dependence on initial velocity, unless you knew T_f =1 sec from the start.
 
Exactly. I feel the same. I think the question somehow lacks specifications with respect to both velocity and time.
Anyways, thanks for your help.
 
I can confirm that you need one of them. Otherwise doubling the velocity and the time difference for a solution scales everything up and leads to a new solution.
 
What if we consider initial velocity = 0? Assuming the calculation starts from the point the bullets were at rest?
 
You can't have a horizontal motion or a 60° angle if you release the bullets at rest. Also, they will never meet then.

Actually, I wonder why the 10 meters are given, they don't seem relevant.
If you assume that the bullets hit each other at the same time they hit the ground, the problem gets a unique solution (assuming the initial velocities are the same).
 
  • #10
Our teachers modified the question giving us the velocity as 5√3 m/s. Would that work?
 
  • #12
Did you find a solution?
 

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