A board 5 feet long slides down a wall. At the instant the bottom end is 4 feet from the wall, the other end is moving down the wall at a rate of 2 feet per second. At the moment, how fast is the bottom end sliding along the ground?

Answer 1

well, you just said math, not calculus, which is why I completed the square to find the vertex of the parabola in the other problem.

3 4 5 triangle
x = 4
y = 3
hypotenuse = 5
dy/dt = -2
=============================
x^2 + y^2 = 25
2 x dx/dt + 2 y dy/dt = 0
dx/dy = -(y/x)dy/dt
= -(3/4)(-2) = +3/2
= +1.5 feet/second