What Determines the Flight Time of Projectiles with the Same Horizontal Range?

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The discussion revolves around the flight time of two projectiles that cover the same horizontal range, with unknown launch velocities and angles. The context is projectile motion, specifically focusing on the relationship between horizontal range and flight time.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of having the same horizontal range while questioning how this affects flight time. Some suggest that flight times must be greater than zero, while others attempt to relate flight time to initial velocity and angle. There is also discussion about the conditions under which flight times might be equal.

Discussion Status

The discussion is ongoing, with participants offering various interpretations of how flight time relates to the initial conditions of the projectiles. Some guidance has been provided regarding the factors that influence flight time, but no consensus has been reached on the specific relationship between horizontal range and flight time for the given conditions.

Contextual Notes

Participants are working under the assumption that air resistance is negligible, and they are considering arbitrary launch angles and velocities. The implications of these assumptions on the relationship between flight time and horizontal range are being examined.

MaximumTaco
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Two Projectiles are shot through the air, and we don't know the launch velocity or angles. What we DO know is that both projectiles cover the same horizontal range.

What can be said about the flight time of each projectile?

Air Res etc etc is ignored.

Thanks in advance.
 
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Um. I guess you could say that both flight times are greater than zero. Not a whole lot else if both velocity and angle are arbitrary.

cookiemonster
 
the time would then be the distance where it landed divided by the intial velocity times cosine of the angle. In other words
t=x/(vcos {theta})

i don't know how else to explain the time it would take.
If one was a vertically thrown object and the other a projectile, then the times would have been the exact same.
 
Well, for the first part of this, two projectiles were fired with arbitary velocity/angles, but with them both reaching the same height. Thus itcan be shown that they were both airborne for the same time, even though the horizontal range is different. Well,i hope so. But can any similar relationship be shown in the second case?
 
No. The flight time depends only on the initial vertical velocity. That can correspond to any total velocity depending on the angle at which the projectiles are fired.

cookiemonster
 

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