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

[MaximumTaco]

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.

 

[cookiemonster]

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

 

[Aerospace]

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.

 

[MaximumTaco]

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?

 

[cookiemonster]

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