Shadow length problem need help badly?!?

Question

A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. When he is 10 feet above the ground,


a) at what rate does the tip of the shadow moving

for the tip why are you trying to find the whole length? Shouldnt you only try to find the part for the shadow?

the answer is 25/3 but i need help for explaining what the tip of the shadow means in this problem.

Answer 1

Try www.Math.com on the upper left hand side click on what level of math you are in, then find an example for your problem.

Hope it helps!

Answer 2

How a man of 6 feet tall can be 10 feet above the ground. He is 10 feet away from the foot of lamp.

Draw the diagram.

Let ABC represents right angled triangle.

let AB = height of the lamp = 15 ft

B is foot of lamp

let C represents tip of shadow when he is 10 feet away from lamp.

Let the point D on BC represents the position of man.

draw perpendicular ED from E on AC to BC.

DE = height of person = 6 feet

let CD = length of shadow = x

let BD = distance between person and light = y

now ABC and CDE are similar triangles.

BC/CD = AB/ED

(x + y)/x = 15/6

6(x+y) = 15x

6x + 6y = 15x

6y = 9x

y = (9/6)x

y = (3/2) x

differentiate with respect to time

dy/dt = (3/2) dx/dt

but dy/dt = 5 ft/s

5 = (3/2) dx/dt

dx/dt = 10/3 ft/s

So the shadow is changing at the rate of 10/3 ft/s

so the rate of change of tip of shadow =

dx/dt + dy/dt = (10/3) + 5 = 25/3 ft/s

Answer 3

This is a similar triangle problem. Let y be the distance the man is from "light pole" and x the length of the shadow. ? what is d(y+x)/dt, ie how fast is the tip moving? Use the triangles to get the relations between the variables.

Answer 4

the tip is dT/dt= dx/dt + dy/dt ... big T is for shadow Tip

So first you have to find dx/dt first by using proportion 6/x=15/x+y

so you get 9x=6y then use implicet differention

9dx/dt= 6dy/dt plug in 5 for dy/dt cause thats hot fast the guy is moving

dx/dt= 30/9 = 3.333

now for dT/dt= dx/dt + dy/dt

Dt/dt= 30/9 + dy/dt which is 5 so now...

30/9 + 45/9 = DT/dt
= 75/9
=25/3 horay

Answer 5

if he is 10 feet off the ground, put Krytonite in his pocket
and bring him back down to earth

LOL - need to re write your question