A man 6ft tall walks at the rate of 5ft/sec towards a street lamp that is 16 ft above the ground. At what rate

Question

is the tip of his shadow moving? At what rate is the length of his shawdow changing when he is 10ft from the base of the light?

Answer 1

Consider the two triangles, (light, base of light, tip of shadow) and (man's head, man's feet, tipof shadow. They are similar triangles, oriented identically, with altitudes 16 and 6 ft respectively. The velocity of the tip of the shadow Vs = velocity of man's head Vm * 16/(16-6) = 8 ft/s. The rate of change of the length of the shadow is Vs - Vm = 3 ft/s. This is independent of his distance from the light.

Answer 2

35