related rates

Question

If a 13 foot ladder is leaning against a vertical wall and the bottom is moved away from the building at 2 feet per second, how fast is the ladder sliding along the wall at the time the bottom of the ladder is 5 feet away from the building? 

Answer 1

x^2 + y^2 = 13^2 = 169

 

2x dx/dt  + 2y dy/dt = 0

 

x dx/dt + y dy/dt = 0

 

(5)(2) + (12) ( dy/dt) = 0    <---- 5^2 + y^2 = 169 ----> y^2 = 144 ----> y=12 when x=5

 

10 + 12 ( dy/dt) = 0

 

dy/dt = -10/12 = -5/6 <--- it is going down, so negative