My Math Forum Related Rate Problem

 Calculus Calculus Math Forum

 June 23rd, 2012, 03:29 PM #1 Senior Member   Joined: Jan 2012 Posts: 159 Thanks: 0 Related Rate Problem I keep getting the height to be 143 cm using similar triangles and differentiating. I am reading up on latex now to type up my steps.
June 23rd, 2012, 04:07 PM   #2
Senior Member

Joined: Feb 2009

Posts: 1,519
Thanks: 3

Re: Related Rate Problem

Quote:
 A spotlight on the ground shines on a wall 1,000 cm away. A boy walks from the spotlight toward the wall at a speed of 120 cm/sec. At the moment when the boy is 400 cm from the wall, the length of his shadow on the wall is decreasing at 46 cm/sec. How tall is the boy?
Comparing the triangles, you get the following proportion:
the height of the boy : his distance from the spotlight :: the height of his shadow : the distance from the wall to the spotlight

Letting h be the height of the boy, x be his distance from the spotlight, and s be the height of his shadow, h/x = s/1000.
Hence $\frac{\mathrm{d}s}{\mathrm{d}t}= 1000h \frac{\mathrm{d}}{\mathrm{d}t}(\frac1x)=1000h(-\frac{1}{x^2})\frac{\mathrm{d}x}{\mathrm{d}t}$.

Substitute ds/dt = -46, dx/dt = 120, and x = 600, then solve for h.

 June 23rd, 2012, 04:46 PM #3 Senior Member   Joined: Jan 2012 Posts: 159 Thanks: 0 Re: Related Rate Problem thanks man my mistake was not treating 1000h like a constant which it is since it does not depend on time. THANK YOU!

 Tags problem, rate, related

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post davedave Calculus 1 November 22nd, 2010 01:53 PM -DQ- Calculus 2 June 5th, 2010 04:34 AM latzi Calculus 1 July 25th, 2009 05:07 AM pranavpuck Calculus 2 December 3rd, 2008 01:16 PM mangox Calculus 9 October 25th, 2008 01:50 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top