Question

could someone just explain how this answer was derived? Answer and work is there but i'm so sleepy that my mind isn't processing everything><

Answer 1

Well, the first thing needed is an equation that relates all the variables. The easy one to pick was the pythagorean theorem since x^2 + y^2 = z^2 has a direct link to all the variables. Next they solved for y. Now in order to find the change in something (how fast the ladder is falling), they need to take the derivative of their equation that they came up with. So x^2 + y^2 =z^2 became 2x(dx/dt) + 2y(dy/dt) =2z(dz/dt). Now the length of the ladder is always 10, so dz/dt is 0, making all of the z'sdisappear completely. The values of x, y, and dx/dt are known, so you plug those in and get 2(6)(1) + 2(8)dy/dt = 0. From there it's just solving for dy/dt
12 = -16(dy/dt), so (dy/dt) = -3/4