A transport plane takes off from a level landing field with twogliders in tow, o

Question

A transport plane takes off from a level landing field with twogliders in tow, one behind the other. The mass of each glider is705 kg, and the total resistance (air dragplus friction with the runway) on each may be assumed constant andequal to 2510 N. The tension in thetowrope between the transport plane and the first glider is not toexceed 11,850 N.
(a) If a speed of 40 m/s is required fortakeoff, what minimum length of runway is needed?
1 m

(b) What is the tension in the towrope between the two gliderswhile they are accelerating for the takeoff?
2 N
(a) If a speed of 40 m/s is required fortakeoff, what minimum length of runway is needed?
1 m

(b) What is the tension in the towrope between the two gliderswhile they are accelerating for the takeoff?
2 N

Explanation / Answer

. 01.   What a fun problem ! 02.   F = (mass)*(acceleration) 03.   Fmax = (2)*(705kg)*(acceleration) + (2)*(2510 Newtons) = 11850.0Newtons    ;   solve foracceleration 04.   = acceleration = [(11850.0Newtons)-(2*2510.0 Newtons)]/(2*705 kg) = 4.843972m/s2 05.   v = velocity = 40 m/s = v0 +*t = 0.0 m/s + (4.843972m/s2)*t      ;   solvefor t 06.   t = (40 m/s)/(4.843972 m/s2)= 8.257687 seconds 07. d = d0 + v0*t +(1/2)*()*t2 08. d = 0.0 meters + (0.0 m/s)*(8.257687 seconds)+ (1/2)*(4.843972 m/s2)*(8.257687seconds)2 09.   d = 165.15 meters . 10.   T = tension between gliders =(705kg)*(4.843972 m/s2) + 2510.0 Newtons = 5925.0 Newtons . 02.   F = (mass)*(acceleration) 03.   Fmax = (2)*(705kg)*(acceleration) + (2)*(2510 Newtons) = 11850.0Newtons    ;   solve foracceleration 04.   = acceleration = [(11850.0Newtons)-(2*2510.0 Newtons)]/(2*705 kg) = 4.843972m/s2 05.   v = velocity = 40 m/s = v0 +*t = 0.0 m/s + (4.843972m/s2)*t      ;   solvefor t 06.   t = (40 m/s)/(4.843972 m/s2)= 8.257687 seconds 07. d = d0 + v0*t +(1/2)*()*t2 08. d = 0.0 meters + (0.0 m/s)*(8.257687 seconds)+ (1/2)*(4.843972 m/s2)*(8.257687seconds)2 09.   d = 165.15 meters . 10.   T = tension between gliders =(705kg)*(4.843972 m/s2) + 2510.0 Newtons = 5925.0 Newtons .

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