helllo
PLEASE HELP! PROBLEM ON RELATED RATES :)
A ball is located at point Q on top of a flagpole 10m above the ground. a light is being raised vertically at the rate of 5 m/s casting the shadow of Q on the ground. how fast is the shadow moving along the ground when the light is 50m high?
Delete
Share
This Question is Closed
beens
Best Response
You've already chosen the best response.
0
where is the light initially?
helllo
Best Response
You've already chosen the best response.
0
20 meters from the flagpole!
coming from the top
amistre64
Best Response
You've already chosen the best response.
0
dL/dt = 5 ....dh/dt = 0 dx/dt =?
dx/dt = dx/dL * dx/dt
find dx/dL ?? maybe not tho.....
helllo
Best Response
You've already chosen the best response.
0
beens
Best Response
You've already chosen the best response.
0
is there an initial height of the light?
amistre64
Best Response
You've already chosen the best response.
0
ahhh...... the shadow moving problem in all the textbooks :)
rejanae13
Best Response
You've already chosen the best response.
0
well you need to cross multiply and divide. so it would be 20m/50m by 5m/x.... that would be 50x by 100... divide 50 by 100 to get x alone and you get x=2
amistre64
Best Response
You've already chosen the best response.
0
thats a rough drawing by the way :)
amistre64
Best Response
You've already chosen the best response.
0
h/(20+x) = 10/(x) if that helps :)
helllo
Best Response
You've already chosen the best response.
0
lol sorry thats what was given to me :p
amistre64
Best Response
You've already chosen the best response.
0
y = (200+10x)/x
amistre64
Best Response
You've already chosen the best response.
0
dx/dt = x^2(dy/dt)/-200 ?? maybe
amistre64
Best Response
You've already chosen the best response.
0
dy/dy = 5
amistre64
Best Response
You've already chosen the best response.
0
x=5
amistre64
Best Response
You've already chosen the best response.
0
im gonna take a gander and say... 25(5) = 125
125/-200 = ?? -.0625 ??
if I did it right lol
amistre64
Best Response
You've already chosen the best response.
0
i think I got the "equation" wrong at the start....
helllo
Best Response
You've already chosen the best response.
0
lol thank you! ..but i dont understand
how can you have dy/dy? :s
helllo
Best Response
You've already chosen the best response.
0
lol so the whole thing is wrong??
amistre64
Best Response
You've already chosen the best response.
0
:) fat fingers...little tiny keyboard :)
helllo
Best Response
You've already chosen the best response.
0
LMAO! ohhhh i see (:
amistre64
Best Response
You've already chosen the best response.
0
it may be right, but I dont trust it yet.... need to find the equation to derive; then the rest is easy.
helllo
Best Response
You've already chosen the best response.
0
ya but thats the part i cant get! wahh :(
amistre64
Best Response
You've already chosen the best response.
0
I am thinking it is the relation of congruent triangles; "y" being the height of the lamp:
x = length of shadow.
10/x = y/(20+x) is what I come up with; there is no question about the distance of the light to the tip of the shadow...
amistre64
Best Response
You've already chosen the best response.
0
10(20+x) = y(x)
(200+10x)/x = y
200/x + 10 = y
200/x = y-10
200/(y-10) = x ??? sounds good
amistre64
Best Response
You've already chosen the best response.
0
this relate y and x..... now implicit it with respect to time right?
helllo
Best Response
You've already chosen the best response.
0
yea thats what i gotta do
helllo
Best Response
You've already chosen the best response.
0
and thank youuu!
for everything so far btw!
amistre64
Best Response
You've already chosen the best response.
0
-200(dy/dt) / (y-10)^2 = dx/dt
dy/dt = 5
y = 50;
amistre64
Best Response
You've already chosen the best response.
0
no prob; I live to math things up lol
amistre64
Best Response
You've already chosen the best response.
0
-0.625 is what i get, and I am almost sure its right... but i get that nagging feeling that I am just being stupid :)
helllo
Best Response
You've already chosen the best response.
0
hahaha but where did u get negative two hundred?
amistre64
Best Response
You've already chosen the best response.
0
ok.... step it out....
200
x = -------
(y-10)
(y-10)(0) - (200)(dy/dt)
dx/dt = ----------------------
(y-10)^2
helllo
Best Response
You've already chosen the best response.
0
lol im on the phone with my friend trying to figure this out and im reading her what u wrote and we both agreed your funny, just thought id let you know :p
but yea we dont understand also where you got the 50 from? (:
care to explain?
amistre64
Best Response
You've already chosen the best response.
0
-200(dy/dt)
dx/dt = -------------
(y-10)^2
amistre64
Best Response
You've already chosen the best response.
0
when y=50...its right there :)
amistre64
Best Response
You've already chosen the best response.
0
dy/dt is given already as the rate of change in "y"... = 5 m/s
amistre64
Best Response
You've already chosen the best response.
0
as y rises; x shrinks.... so its (-) direction..
helllo
Best Response
You've already chosen the best response.
0
ohhh okay!
thank you so so much
honestly, it means a lot (: (:
amistre64
Best Response
You've already chosen the best response.
0
just let me know if im right :)
helllo
Best Response
You've already chosen the best response.
0
i will haha
but its the first time im on this site so how can i tell you?
helllo
Best Response
You've already chosen the best response.
0
because i have to check with my teacher first
amistre64
Best Response
You've already chosen the best response.
0
shout really loud? :) AMISTRE WAS RIGHT!!!.... or if im wrong it would be: AMISTRE WAS WRONG .... ill feel it either way :)
helllo
Best Response
You've already chosen the best response.
0
LMAOOOOOOOOO!
amistre64
Best Response
You've already chosen the best response.
0
that moving shadow thing is in all the calc textbooks If seen, and it always makes me nervous
helllo
Best Response
You've already chosen the best response.
0
lol im sure you got it right though, it seemed to make sense. i found it impossible!
amistre64
Best Response
You've already chosen the best response.
0
good luck :)
helllo
Best Response
You've already chosen the best response.
0
thank you again!:)