Related Rate Shadow & Spotlight Question
I have a question that I am stuck on for the Related Rates problems. I did it and got a negative answer when it's suppose to be positive I did it again a little differently and still got a negative answer!! Here is the problem:
Joe is 1.8 meters tall is walking directly towards a spotlight located on the ground 20 meters away from the theatre. If Joe walks at a constant rate of 1/5 m/s find the rate at which the length of his shadow on the wall is changing when he is 6 meters from the lamp.
So the 2nd time I went through it I set it up as:
Given: dx/dt = 1/5 m/s
Find: dy/dt when x = 6
y/20 = 1.8/20-x
y = 36/(20-x)
dy/dt = [-36/(20-x)^2](dx/dt)
dy/dt = [-36/(20-6)^2](1/5)
dy/dt = -9/245
Worked from there. First time I got an answer of -1/5, second time an answer of -9/245. But I know if he is moving towards the spotlight the answer will have to be a positive rate. I think there is something fundamentally wrong with my procedure, if anyone could show me their through process on this I would greatly appreciate it!