I have problem with this question :/
a 2 meter high plank stands on the distanse 3 meter from a wall. Decide the shortest lenght a ladder must have to reach from the ground to the wall. (the wall and the plank is vertikal and the ground is horisontel.)
the right answer is (3 + ^3(12^0.5) (1+(4 / 12^2/3))^0.5 but i dont get it :/
i did this way:
i say that the distance from the plank to the ladder is x
L^2 = (3+x)^2 + (6/x + 2)^2
2L`= 2(3+X) + 2(6/x + 2)(-6/x^2)
L´= 0 => x4 + 3x^3 - 12x - 36 = 0
i dont know more, help please
I interpret this as meaning that the "2 meter high plank" forms a barrier three feet from the wall that the ladder must clear.
Let x be the distance from the plank to the foot of the ladder, and y the height that the ladder reaches on the wall. Assuming the ladder just clears the barrier, we have, by "similar triangles", .
Essentially, then, you want to minimize the length of the hypotenuse, subject to the condition that . I don't see any good way to do that without Calculus.