Related rates ladder problem

Question

A ladder 7ft long is leaning on a wall. At some point the bottom part starts to slide on the floor at a speed of 4ft/sec. What is the speed at which the top part is sliding down on the wall when it is at 2 ft of distance from the floor?

Answer 1

Make a little sketch of a triangle with legs x and y and hypotenuse 7

then x²+y²=49

 

2x(dx/dt) + 2y(dy/dt) = 0

 

Given: dx/dt = 4

Want: dy/dt when y = 2.

 

When y = 2, x = 3√5

 

dy/dt = (dx/dt)(-x/y) = (4)(-3√5)/2.

 

Answer: dy/dt = -6√5 ft/sec