Answer
(a) The minimum length of the runway is 160 meters.
(b) $T = 6000~N$
Work Step by Step
(a) Let's consider the system of both gliders. Let's assume that the tension in the first rope is 12,000 N. We can find the acceleration.
$\sum F = ma$
$12,000~N - 2500~N-2500~N = ma$
$a = \frac{7,000~N}{1400~kg} = 5.00~m/s^2$
We can find the minimum length of the runway.
$x = \frac{v^2-v_0^2}{2a} = \frac{(40~m/s)^2-0}{(2)(5.00~m/s^2)}$
$x = 160~m$
The minimum length of the runway is 160 meters.
(b) Let's consider the system of the second glider.
$\sum F = ma$
$T - 2500~N = ma$
$T = (700~kg)(5.00~m/s^2) + (2500~N)$
$T = 6000~N$
