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Unknown9
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Homework Statement
A spotlight on the ground shines on a wall 12 m away. If a man 2m tall walks from the spotlight toward the building at a speed of 1.6m/s, how fast is the length of his shadow on the building decreasing when he is 4m from the building?
Homework Equations
x2 + y2 = z2
The Attempt at a Solution
So the x and y values are decreasing, the x at 1.6m/s which is dx/dt with respect to time. We want to find out what dy/dt is which is how fast the shadow is decreasing.
so using x2 + y2 = z2
plug in 12m for x
144 + y2 = z2
implicit differentiate that equation and I get
2y*(dy/dt) = 2z*(dz/dt)
solve for (dy/dt)
(dy/dt) = (2z*(dz/dt))/2y
now I believe we plug in 2m for y at that point which would be
(dy/dt) = (2z*(dz/dt))/4
this is where I start to get lost. I don't know what to plug in for z, or dz/dt to get dy/dt