HW 8 Solutions - Mathematics 408K: Homework 8 Gagan Tara...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Mathematics 408 K: Homework 8 Gagan Tara Nanda 09 th October, 2004 HW 8 : # s 8 , 10 , 12 , 20 , 21 , 22 8. I’ve clipped the diagram below from the original solutions, so to have it match my question, change the length 5 in the diagram to 8 ,s incetheis landinmyquest ionis 8 miles from the shore. In this setup, x isthed istanceofthel ightbeam ’sendpo intfromtheleftedgeoftheshorel ine .Wewant to know how fast the beam is travelling along the shore line, so we want to f nd dx dt . From the diagram, tan θ = x 8 x =8tan θ . Di f erentiate implicitly with respect to t to get dx dt =8sec 2 d θ dt . Observe that 1 revolution is 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Gagan Tara Nanda 2 which is d θ dt . Hence dx dt =8 s e c 2 θ (8 π ) = 64 π cos 2 θ . At the particular instant requested, the beam makes an angle of 45 with the shoreline, which is 90
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

HW 8 Solutions - Mathematics 408K: Homework 8 Gagan Tara...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online