ps11sol - 18.02 Fall 2008 – Problem Set 11, Part B...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 18.02 Fall 2008 – Problem Set 11, Part B Solutions 1. a) North of 42 ◦ N is 0 ≤ φ < φ , where φ = (90 − 42) π/ 180 radians. integraltext 2 π integraltext φ sin φ dφdθ integraltext 2 π integraltext π sin φ dφdθ = integraltext φ sin φ dφ integraltext π sin φ dφ = − cos φ − ( − 1) 2 ≈ . 165 About 16.5 percent of the Earth’s surface is north of Boston. b) First take the average of φ : ¯ φ = integraltext 2 π integraltext π π/ 2 φ sin φ dφdθ integraltext 2 π integraltext π π/ 2 sin φ dφdθ = π − 1 because integraltext π π/ 2 sin φ dφ = 1, and, by integration by parts, integraldisplay π π/ 2 φ sin φ dφ = − integraldisplay π π/ 2 ( − cos φ ) dφ + ( − cos φ ) φ vextendsingle vextendsingle vextendsingle π π/ 2 = π + integraldisplay π π/ 2 cos φ dφ = π − 1 Thus ¯ φ = π − 1 radian and the average latitude is 32 . 7 ◦ S. The closest large cities are Santiago, Chile (33 . 4 ◦ S) and Perth, Australia (31 .....
View Full Document

This note was uploaded on 04/28/2009 for the course MATH 18.02 taught by Professor Auroux during the Fall '08 term at MIT.

Page1 / 3

ps11sol - 18.02 Fall 2008 – Problem Set 11, Part B...

This preview shows document pages 1 - 2. Sign up to view the full document.

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