Question

A street light is at the top of a 12 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 40 ft from the pole?

Speed of tip of her shadow = ___ ft/sec

Answer 1

What level math is this?

Answer 2

Calculus.

Answer 3

Derivatives and related rates.

Answer 4

Oh sorry I'm not in calculus..

Answer 5

Oh I just did those....this should help, its the same question with one different numebr :)
http://openstudy.com/study#/updates/4f949b60e4b000ae9ecad05f

Answer 6

It's okay.

Answer 7

number*

Answer 8

i think u need to use v=dX/dt
to identify the speed of the tip of her shadow

Answer 9

that's the the instantaneous velocity

Answer 10

\[{18\over{d+s}}={6\over s}\] which should give you \(18s=6d+6s\)

Answer 11

now derive that and then i believe (not so sure, but-) that \(dd\over dt\) is supposed to be the 7 ft/sec since she's walking away -distance from the pole is increasing at the rate of- at a speed of 7 ft/sec

Answer 12

\[18s=6d+6s\]\[18{ds\over dt}=6{dd\over dt}+6{ds\over dt}\]\[{ds\over dt}(18-6)=6(7)\]^ i pulled out the \(ds\over dt\) from the 18 and 6 after i subtracted the 6\(ds\over dt\) and then plugged in 7 ft/sec for the \(dd\over dt\)\[{ds\over dt}={6(7)\over(18-6)}\]\[{ds\over dt}={42\over12}\]\[{ds\over dt}={7\over2}ft/sec\]

Answer 13

I'm really not sure if this is supposed to be the final answer @Jwoodward48 - sorry. But, i know the work I've done so far is correct...I hope this helps, and if it's possible, check the answer out in like the back of your book or something, or ask a friend what they got
Sorry i couldnt help out too much

Answer 14

It isn't correct, but thanks for trying.

Answer 15

what's the actual answer?

Answer 16

I'm still trying to figure it out.

Answer 17

then how do you know it's wrong o.O

Answer 18

the only other thing i can think of is the fact that you probably have to add her speed to the speed of her shadow...so that would be \({7\over2}+7\)\[={21\over2}ft/sec\]

Answer 19

i think she got the answer correct

Answer 20

@Jwoodward48 the answer is \({21\over2}ft/sec\)

Answer 21

I get the feeling you're not satisfied @Jwoodward48

Answer 22

he has to be

Answer 23

are u alright there bro?

Answer 24

incorrect...

Answer 25

It was 14!

Answer 26

how do you know it's wrong...i'm confused
and how is it 14?

Answer 27

d=s

Answer 28

Because of related rates.

Answer 29

....i give up...for a second there i actually thought i was smart again..oh well

Answer 30

12(l)=6(x+l) (you are smart, you used math to get an answer)

Answer 31

12l-6l=6x

Answer 32

6x=6l

Answer 33

x=l

Answer 34

dx/dt=dl/dt

Answer 35

dx/dt=7

Answer 36

I want dl/dt+dx/dt, which is 2 * dx/dt

Answer 37

=14!

Answer 38

next time, you already know what u should be doing
we learn from our mistakes D:

Answer 39

Yep!

Answer 40

i took calculus last year, so i really don't have a complete understanding of it