Question
11. A person 1.8 m tall walks away from a spotlight 10 m above the ground at a rate of 1.5 m/s. How fast is the length of the person's shadow increasing when the person is 9 m from the spotlight?
Answers
oobleck
if the shadow's length is s, then using similar triangles, when the person is x meters from the pole,
s/1.8 = (s+x)/10
10s = 1.8s + 1.8x
s = 2/9 x
so ds/dt = 2/9 dx/dt
you know that dx/dt = 1.5, so now just finish it up
s/1.8 = (s+x)/10
10s = 1.8s + 1.8x
s = 2/9 x
so ds/dt = 2/9 dx/dt
you know that dx/dt = 1.5, so now just finish it up