Question

A person 6 ft tall stands 10 ft from point P directly beneath a lantern hanging 30 ft above the ground, as shown in the figure below. The lantern starts to fall, causing the person’s shadow to lengthen. Given that the lantern falls 16t2 ft in t seconds, how fast will the shadow be lengthening when t = 1?

Answer 1

I honestly wish this was an april fools joke....

Answer 2

it looks doable, you got the pic?

Answer 3

usually this is just a matter of relating similar triangles

Answer 4

Sent it in a message cuz it gives away the school I'm at lol

Answer 5

yeah I set it up as 6/x=30/x+10

Answer 6

thats not a lantern; thats the sun lol

Answer 7

.....

Answer 8

lol

Answer 9

its the lantern you got me thinking for a sec

Answer 10

dL/dt would be 16 correct? but I don't get how to put a dL/dt in there lol

Answer 11

similar triangles does look like the key:

6 is to 30-d
as
s is to s+10

(s+10)/s = (30-d)/6 ; since we want s'; lets take the derivative and solve for s' but im gonna rewrite it

1+10/s = 5 -d/6

-10s'/s^2 = -d'/6

s' = d' s^2/60

we agree so far?

Answer 12

dL, as you call it; is 32t i believe

Answer 13

hmmm sec let me see if I get what you are saying

Answer 14

how did yo uget 1+10/s=5-d/6

Answer 15

ill splain that after i post this since i already typed it :)

all this happens when t=1 soo

im gonna go ahead and use the usual gravity version of this:

-16t^2 + 30 at t = 1; 14

6 14
-- = -----
s s+10

6s+60 = 14s

60 = 8s

s = 7.5

Answer 16

AH i got the part i just asked about lol

Answer 17

by comparing like sides of the similar triangles we get:\[\frac{6}{s}=\frac{30-d}{s+10}\]

good

Answer 18

\[s' = d' \frac{s^2}{60}\]

\[s' = d' \frac{(7.5)^2}{60}\]

d = 16t^2; so d' = 32t at any given t; when t=1; d' = 32

\[s' = 32 \frac{(7.5)^2}{60}\]

\[s' = 4 \frac{(7.5)^2}{7.5}\]

\[s' = 4(7.5)\]

maybe

Answer 19

This is way too hard for non-eng students to be doing lol thats the correct answer

Answer 20

you're too smart

Answer 21

yay!! lol

Answer 22

i am, ive been trying to dumb myself down by watching 3 and a half men tho so there is hope ;)

Answer 23

hahaha out of curiosity are you are grad student or math teacher or something? You always answer the most difficult questions like you are serving cake

Answer 24

im an undergraduate at the moment, working towards a BA in math so that i can go for the masters and beyond

Answer 25

You must be at harvard or an ivy or something you are a damn genius!

Answer 26

:) well, i apparently did it right on this one but forgot how to do it by today

Answer 27

ahh, that 30-d part ....