A man pulls a five-meter plank up the side of a building under construction with a rope tied to one end of the plank. Assume the opposite end of the plank follows a path perpendicular to the wall of the building, and the man pulls the rope at a rate of 2 metres per second. How fast is the end of the plank sliding along the ground when it is 4 metres from the wall of the building?
Variables:
x = distance from base of plank to base of wall= 4 metres
y = height of top of plank.
Rates are:
= rate the end of the plank slides along the ground
= rate at which the top of the plank rises = 2
m/sec.
Equation- 
Solve for Y:
+
= 
16 + = 25
= 9 = 3(3)
y = 3
Differentiate-
2x + 2y = 0
x
+ y
= 0
Solve:
x + y = 0
(4) 
+ 3(2) = 0
+ 
= 0
= 
= - metres/sec
The reason the answer is negative is because the length between the end of the plank and the wall is getting smaller.
