How Much Runway is Needed for a Plane Towing Two Gliders to Take Off?

[MrKoffee]

A transport plane has two gliders tied behind it. The max force allowable on the tow rope is 12000N. The mass of each glider is 700kg. A velocity of 40 m/s is required to take off. What is the minimum runway space required.


The solution I have arrived at doesn't seem correct, hopefully someone can tell me where I have strayed off the path.

F = ma

12000 = (700+700)a
a = 12000/1400
a = 8.57 m/s^2



V = V(init) +at

40 = 0 +8.57t
t = 40/8.57
t = 4.67s



S = 1/2(a)t^2+V(init)t + S(init)

1/2(8.57)(4.67^2) + 0 + 0 = 20 meters


I don't think the plane could reach 40 m/s in 4.67 seconds and it would have to be a really small transport plane to take off in 20 meters. Hopefully someone can point out where I went wrong.

Thanks for the help.

 

[Fermat]

You forgot to square the 4.67 value. It should be about 93m

4.67s does seem a bit short, but 93 m seems ok!

 

[MrKoffee]

Huh, After checking my work a few times I still missed that one. Thanks!