A man 6 feet tall walks at a rate of 5 feet per second toward a street light that is 16 feet tall. At what rate is the length of his shadow

street-light
shadow-changing

#1

A man 6 feet tall walks at a rate of 5 feet per second toward a street light that is 16 feet tall. At what rate is the length of his shadow changing when he is 10 feet from the base of the light?

Answer:

draw a line from light top to man top extentending to ground.
. a triangle is formed . let size of shadow be x and distance between man and pole be y at any time t.
u see that . x/(x+y)=6/16
or 5x=3y
differentate wrt t
5dx/dt=3dy/dt

dy/dt= 5

5dx/dt=15
dx/dt=3