A transport plane takes off from a level landing field with two gliders in tow, one behind the other. The mass of each glider is 700 kg, and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 4300 N. The tension in the towrope between the transport plane and the first glider is not to exceed 12000 N.

If a speed of 40 m/s is required for takeoff, what minimum length of runway is needed?

Question

Physics

Sonny Harrison

5 October, 16:21

A transport plane takes off from a level landing field with two gliders in tow, one behind the other. The mass of each glider is 700 kg, and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 4300 N. The tension in the towrope between the transport plane and the first glider is not to exceed 12000 N.

If a speed of 40 m/s is required for takeoff, what minimum length of runway is needed?

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Answers (1)

Know the Answer?

Esperanza Kerr · Answer 1

Length = 155.6 m

Explanation:

given data

mass = 700 kg

total resistance = 4300 N

tension = 12000 N

speed = 40 m/s

solution

we get here equation for glider in the back and front

for the glider in the back

T - 2400 = 700 a ... 1

for the glider in front

12000 - T - 2400 = 700a ... 2

now we add both these equations

12000 - 4800 = 1400 a ... 3

a = 5.14 m/s²

and

now we use equation of motion

v² - u² = 2 a S ... 4

40² = 2 * 5.14 * S

so

Length = 155.6 m