Answer to Question #336364 in Calculus for John

Question

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

A light is hung 15 feet above a straight horizontal path. If a man 6 feet tall walking

away from the light at a rate of 5 feet per second, how fats is the man’s shadow

lengthening when the man is 8 feet from the base of the light source?

PLEASE ANSWER MY QUESTION QUICKLY!!

DEADLINE : 05/03/2022 11 : 00 PM

Answer 1

x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. i assume the man and pole are standing straight up, which means the 2 triangles are similar.

$\frac{y-x}{y}=6/15$

$15y-15x=6y$

$y=5/3x$

differentiate both sides with respect to

t or time.

$dy/dt=(5/3)( dx/dt)=5/3\times5=25/3 ft/sec$

actually, the man's distance from the base doesn't matter since only his speed affects how fast his shadow moves.