A woman 5 ft tall walks at the rate of 7.5 ft/sec away from a streetlight that is 10 ft above the ground. At what rate is the tip of her shadow moving?
Height of the woman = 5 ft Rate at which the woman is walking = 7.5 ft/sec Let us assume the length of the shadow = s Le us assume the distance of the woman's feet from the base of the streetlight = x Then s/5 = (s + x)/12 12s = 5s + 5x 7s = 5x s = (5/7)x Now let us differentiate with respect to t ds/dt = (5/7)(dx/dt) We already know that dx/dt = 7/2 ft/sec Then ds/dt = (5/7) * (7/2) = (5/2) = 2.5 ft/sec From the above deduction, it can be easily concluded that the rate at which the tip of her shadow is moving is 2.5 ft/sec.
