Latitude

[kpham123]

11Q-26. At what latitude north of the equator is the average length of a time zone such as the Central Time Zone equal to 600 miles?
couldnt find anything from a search on google on timezone length
from recent tournament at Dulles HS TMSCA #9

[kpham123]

Problem #2 which I might as well post here:
11Q-38. Mercury circles the sun every 87.99 days, Mars every 686.98 days, and Jupiter every 4332.4 days. How many revolutions around the sun does Mercury make between the times of closest approach of Jupiter to Mars?

[calcguy]

11Q-26. The average length of a time zone is 1/24th of the circumference of the latitude circle (Latitude "lines" are circles with centers on Earth's axis).
The equator is the 0° latitude circle. All other latitude circles have radii equal to the radius of the Earth (3960 mi) times the cosine of the latitude angle.
Here's the solution: 600 = 1/24 x 2π x 3960 x cosΘ → Θ = 54.6°

11Q-38. The given orbital periods have units of days/revolution. The reciprocal of the period is the rotational frequency with units revolutions/day. You can calculate the time between closest approach of Jupiter to Mars by dividing 1 revolution by their relative frequencies (subtract their rotational frequencies to get relative frequency) like this: 1/(1/686.98 - 1/4332.4) = 816.44 days. Now divide this time by Mercury's orbital period: 816.44/87.99 = 9.279 revolutions.