Calc Problem [Related Rates] - Tilted Forum Project Discussion Community

Artsemis · 02-25-2005, 12:03 AM

Problem
--------
A spotlight on the ground shines on a wall 12m away. If a man 2m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4m from the building?

What I did
----------
I used related triangles to say:
x/2 = 12/y
xy=24

Taking the derivitive of both sides, I get:
x(dy)+y(dx)=0

Substituting:
3(1.6)+8(dx)=0
*The 8 comes from him being 4m from the wall, which is 12m from the light

4.8+8(dx)=0
8dx=4.8
dx = .6

I know this is wrong, can someone figure this out please? Thanks.

vinaur · 02-25-2005, 05:42 AM

You (almost)get the right answer. Your mistake is in the second to last line. When you move the 4.8 over. That should be negative. 8dx=-4.8 therefore dx=-.6.

Artsemis · 02-25-2005, 07:26 PM

er, yeah... that's what i had on paper.

Basically the instructor gave the problem and the answer and we were to show the work. Well I found out today that the answer the instructor gave was wrong and this was correct :/

Thanks vinaur for the reply

02-25-2005, 12:03 AM	#1 (permalink)
Artsemis Insane Location: West Virginia	Calc Problem [Related Rates] Problem -------- A spotlight on the ground shines on a wall 12m away. If a man 2m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4m from the building? What I did ---------- I used related triangles to say: x/2 = 12/y xy=24 Taking the derivitive of both sides, I get: x(dy)+y(dx)=0 Substituting: 3(1.6)+8(dx)=0 *The 8 comes from him being 4m from the wall, which is 12m from the light 4.8+8(dx)=0 8dx=4.8 dx = .6 I know this is wrong, can someone figure this out please? Thanks. __________________ - Artsemis ~~~~~~~~~~~~~~~~~~~~ There are two keys to being the best: 1.) Never tell everything you know

02-25-2005, 07:26 PM	#3 (permalink)
Artsemis Insane Location: West Virginia	er, yeah... that's what i had on paper. Basically the instructor gave the problem and the answer and we were to show the work. Well I found out today that the answer the instructor gave was wrong and this was correct :/ Thanks vinaur for the reply __________________ - Artsemis ~~~~~~~~~~~~~~~~~~~~ There are two keys to being the best: 1.) Never tell everything you know

02-25-2005, 05:42 AM	#2 (permalink)
vinaur Insane	You (almost)get the right answer. Your mistake is in the second to last line. When you move the 4.8 over. That should be negative. 8dx=-4.8 therefore dx=-.6.