posted by sara on .
A street light is mounted at the top of a 6-meter-tall pole. A man 2 m tall walks away from the pole with a speed of 1.4 m/s along a straight path. How fast is the tip of his shadow moving when he is 16 m from the pole?
same question ....
just change the necessary numbers
since you have a calculus class, you probably ought to do it Reiny's way, but sometimes a little simplification can save you some work:
If the man is x away from pole, ad his shadow length is s, then using similar triangles,
s/2 = (x+s)/6
s = 1/2 x
so, ds/dt = 1/2 dx/dt
since the tip of the shadow is x+s from the pole, it is moving at
dx/dt + ds/dt = dx/dt + 1/2 dx/dt = 3/2 dx/dt = 3/2(1.4) = 2.1 m/s