A 7.00​-ft-tall man walks at 6.00 ​ft/s toward a street light that is 18.0 ft above the ground. At what rate is the end of the​ man's shadow moving when he is 15.0 ft from the base of the​ light?

Question

Use the direction in which the distance from the street light increases as the positive direction.

Answer 1

Get a formula for the shadow's length in terms of time

The shadow's length = x in feet

t= time in seconds

7/x = 18/(x+15-6t) ratios of two sides of similar triangles are equal

solve for x in terms of t; cross multiply

11x = 105 - 42t

x = 105/11 -42t/11

take derivative

dx/dt = -42/11 feet per second = - 3 9/11 ft/sec

The shadow is getting shorter by almost 4 feet every second