at night, a 6ft man is walking towards a 8ft lamp post at a speed of 3ft/sec how fast is his shadow changing?
At distance x, the shadow has length s, so
s/6 = (s+x)/8
s/6 = s/8 + x/8
4s = 3s+3x
s = 3x
ds/dt = 3 dx/dt
so, the length of the shadow shrinks at a constant rate of 9 ft/s.