Solve the given problem.

Question

Ken is 6 feet tall and is walking away from a streetlight. The streetlight has its light bulb 14 feet above the ground, and Ken is walking at the rate of 5.3 feet per second. Find a function, d(t), which gives the distance Ken is from the streetlight in terms of time. Find a function, S(d), which gives the length of Ken's shadow in terms of d.

Answer 1

man 6 feet tall walking from a 14 foot street lamp at 5.3 feet per second

d(t) = distance from base of lamp 5.3t

s(t) = length of shadow at time t

s(d) = length of shadow when d feet from lamp base

construct a right triangle, 14 ft = height d+x = shadow length

it encloses a similar right triangle height = 6 ft, base = x = shadow length

s and d = 0 at t = 0

angle between hypotenuse and base = arctan(6/s) = arctan(14/(x+d)

6/s = 14/(s+d)

14s = 6s+6d

8s =6d

4s =3d

s = 4d/3

s(d) = 4d/3

shadow = 4/3 of distance man is from the lamp

s(t) =4(5.3t)/3 = 21.2t/3