Question

In a glider stunt at an air show, a towing airplane (motorized plane pulling the gliders) takes off from a level runway with two gliders in tow. The gliders are pulled by two tow ropes, the first glider attached to the back of the towing plane and the second glider attached to the back of the first glider. The mass of each glider is 700 kg. The total resisting force (air drag plus friction with the runway) on each glider is equal to 3700 N. The resisting force can be assumed to be constant during the take off. The maximum allowed tension in the tow rope between the transport plane and the first glider is 12000 N. The maximum allowed tension in the second tow rope is the same as the first tow rope.
If the takeoff speed for the gliders and the plane is 40 m/s, what minimum length of runway is needed for take off? Express your answer in meters.

Answer 1

Answer:

minimum length of runway is needed for take off 243.16 m

Explanation:

Given the data in the question;

mass of glider = 700 kg

Resisting force = 3700 N one one glider

Total resisting force on both glider  = 2 × 3700 N = 7400 N

maximum allowed tension = 12000 N

from the image below, as we consider both gliders as a system

Equation force in x-direction

2ma = T -f

a = T-f / 2m

we substitute

a = (12000 - 7400 ) / (2 × 700 )

a = 4600/1400

a = 3.29 m/s²

Now, let Vf be the final speed and Ui = 0 ( as starts from rest )

Vf² = Ui² + 2as

solve for s

Vf² = 0 + 2as

2as = Vf²

s = Vf² / 2a

given that take of speed for the gliders and the plane is 40 m/s

we substitute

s = (40)² / 2×3.29

s = 1600 / 6.58

s = 243.16 m

Therefore, minimum length of runway is needed for take off 243.16 m