Question

Help please: Rate question!
A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?

Answer 1

@tkhunny

Answer 2

We will need to identify the similar triangles.

Side - Pole : Woman :: 15 ft : 6 ft
Angle - Pole/Path vs. Woman/Path
Side - Pole to Light at the end of the shadow vs. Woman to end of shadow.

There it is! Now what?

Answer 3

Yes Find the dy/dt?

Answer 4

Before you can find dy/dt, you must define 'y'. What is it?

Answer 5

6x+6y=15y?

Answer 6

use two tringle?

Answer 7

This is one thing you must learn. You can NOT just write down variables without defining them. What is x? What is y? No one can see into your head. You must communicate what is in there.

Is y the length of the shadow?

Answer 8

Ok, I draw it

Answer 9

There you go! A clue! Now the similar triangles:

\(\dfrac{6}{15} = \dfrac{y}{x+y}\)

We're almost done.

Answer 10

is my drawing wrong?

Answer 11

6x+6y=15y?

Answer 12

Why would you ask that? Your drawing is what it is. It provides the definitions we seek. Now, go with it.

Answer 13

And now, only AFTER we see your drawing, and thus your definitions, can we understand your equation. Now what?

Answer 14

Yes, beacse we are using two triangle.

Answer 15

could you identify what 7ft/sec is ?

Answer 16

speed?

Answer 17

i know but, its dx/dt = 7ft/sec.

Answer 18

No, so far 6x+6y=15y

Answer 19

thats all i understand

Answer 20

she walks away from pole with that speed, so x changes with that speed, so dx/dt =7
got this ?

Answer 21

yes

Answer 22

so theres 2 equation?

Answer 23

now isolate y from 6x+6y=15y
and differentiate it.

Answer 24

6x=9y? is this how do you isolate y?

Answer 25

yeah..then
y=6x/9
now if you take derivative, with respect to 't' what do you get ?

Answer 26

y=6x/9 dt/dx?

Answer 27

no...
dy/dt = 6* (dx/dt)/9
got this ?

Answer 28

yes beacuse its y.... i got it..

Answer 29

now you have dx/dt=7 and you need dy/dt
can you find it ?

Answer 30

d/dt=7*dy/dt?

Answer 31

?
dy/dt = 6* (dx/dt)/9
with
dx/dt=7
gives you
dy/dt = 6* 7/9
-_-

Answer 32

Oh haha I thought it was totally saprate things! ops

Answer 33

so, the shadow is moving with the speed of 14/3 ft/sec....