Keep in mind this is a Top Gun-themed homework assignment.
Cougar comes in for a shaky landing. His 20422 kg airplane traveling at 85 m/s strikes the deck at 3.5 degrees below the horizontal. Cougar's plane snags the landing cable stretched across the deck. The landing cable is a cable which feeds out from beneath the deck of the carrier from two points 15 m apart from each other. The cable is hydraulically controlled so that it maintains a constant tension. The airplane travels forward 60 meters before stopping. Consider the landing cable to be the only thing that stops the aircraft, the wheel brakes are not applied.
Calculate the magnitude of tension in the landing cable.
W = 1/2mv^2 (in this case)
W = ∫Fxdx
The Attempt at a Solution
Since there's no direct way to find tension, I started with W = .5(20422)(85cos3.5)^2, solving for work done by the cable on the plane, which gave me -73499523.13 J. This answer was another part of the question and has been marked as correct.
In order to solve for tension I tried setting 73499523.13 J equal to ∫Tsin(arctan(x/7.5))dx from 0 to 60 meters, or 73499523.13 = T(7.5sqrt(.0177777777(60)^2 + 1)-7.5sqrt(1)).
This gave me T = 73499523.13/(7.5sqrt(65) - 7.5), or 1387649.215 Newtons.
Using my calculator to integrate the tension function and I arrived at the same answer. 1387649.215 N is not the correct answer, so I would like help on this problem, as the rest of my classmates are stumped as well.
I apologize ahead of time for formatting errors and for the lack of illustrations provided in the homework itself.