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

  • Thread starter Thread starter MaximumTaco
  • Start date Start date
  • Tags Tags
    Trajectories
AI Thread Summary
The discussion centers on the flight time of two projectiles that cover the same horizontal range but have unknown launch velocities and angles. It is established that both projectiles will have flight times greater than zero, but the exact relationship between their flight times is complex. The flight time can be calculated using the formula t = x/(v cos θ), where x is the horizontal distance, v is the initial velocity, and θ is the launch angle. If both projectiles reach the same height, they will have the same flight time, but varying angles and velocities can lead to different flight durations. Ultimately, flight time is primarily determined by the initial vertical velocity of the projectiles.
MaximumTaco
Messages
44
Reaction score
0
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.
 
Physics news on Phys.org
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
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Find Projectile Flight Time Given Only Maximum Height
Replies
4
Views
2K
Relationship between horizontal range and angle of launch
Replies
7
Views
3K
Make 2 launchers that shoot a straw with clay at the end
Replies
3
Views
1K
Launching a Projectile with Air Resistance
Replies
13
Views
3K
I need opinions on a Projectile Motion problem that I made up
Replies
11
Views
2K
In the horizontal direction, what is the initial velocity of the projectile?
Replies
1
Views
1K
Relationship between Launch height and range of a projectile
Replies
15
Views
25K
How Do You Solve a Projectile Motion Problem?
Replies
3
Views
4K
Needing some help about time of flight of a launched ball/horiz range
Replies
6
Views
3K
Optimal Angle and Horizontal Range of a Bottle Rocket Projectile
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top