Question

A street light is on top of a 12 foot pole. a person who is 5 feet tall walks away from the pole at a rate of 4 feet per second. at what speed is the length of the person's shadow growing

Answer 1

2 and 6/7 ft/sec or approximately 2.857 ft/sec First, let's make an expression to express the length of the person's shadow as a function of the distance from the light pole. Variables d = distance person is from pole s = length of shadow person is casting. The right triangle that the person makes with their shadow is similar to the right triangle made by the light pole and the end of the person's shadow. So 5/12 = s/(s+d) Now solve for s in terms of d 5/12 = s/(s+d) 5/12(s+d) = s 5s/12 + 5d/12 = s 5d/12 = s - 5s/12 5d = 12s - 5s 5d = 7s 5d/7 = s So for every foot the person walks away from the pole, the shadow increases by 5/7ths of a foot. Since the person is moving at 4 ft/sec, just multiply 5/7 by 4. 5/7 * 4 = 20/7 = 2 6/7 or approximately 2.857142857 ft/sec