Assignment 1 Solutions (Fall 2008)

# Assignment 1 Solutions (Fall 2008) - P207 Fall 2008...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: P207 - Fall 2008 Solutions Assignment 1 1 The apparent size of the elevator is proportional to the angle subtended θ . We see from the diagram that tan θ = h/d where h is the height of the elevator and d is the distance. Since the height is always much h d θ less than the distance, we can use the small angle approximation for the tangent and write that θ ≈ h d (a) The angular size of elevator at various distances is given in the table distance angular size angular size (small angle approximation) (exact) d[km] θ [rad] ∼ h/d θ [rad] = tan- 1 ( h/d ) 8 5 × 10- 3 5 . 000 × 10- 3 4 1 × 10- 2 1 . 000 × 10- 2 2 2 × 10- 2 2 . 000 × 10- 2 1 4 × 10- 2 3 . 998 × 10- 2 0.5 8 × 10- 2 7 . 983 × 10- 2 0.25 1 . 6 × 10- 1 1 . 587 × 10- 1 1 (b) Angular size of 40m grain elevator vs distance. 0.05 0.1 0.15 0.2 2000 4000 6000 8000 10000 θ [rad] distance [m] h/d 2 (c) Log plot of angular size of 40m grain elevator vs distance. The 0.001 0.01 0.1 1 10 2000 4000 6000 8000 10000 θ [rad] distance [m] h/d plot of log( θ ) vs distance is an approximately straight line for distances much greater than the height of the object (say beyond 4000m), suggesting that in that regime, the angular size is very approximately an exponential function of the distance. Of course we know that when h/d 1 that the angular size θ ∼ h/d . Then log( θ ) = log( h )- log( d ) If we were to make a log-log plot, that is plot log( θ ) vs log( d ) then we would get a straight line with slope- 1....
View Full Document

### Page1 / 6

Assignment 1 Solutions (Fall 2008) - P207 Fall 2008...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online