Rising Sun [;)]

GiveATry

City A, is approximately 120 miles due west of City B. They are in the same time zone and at the same elevation. How much sooner would a person in City B see the rising sun than a person in City A?

 

salmonfish

R(earth)=3950 miles; Treat sun as a point farfar away from earth. Earth spin angular rate= 2pi/(24x3600) (弧度/秒），then, angle A=120/3950=0.03038 (弧度） therefore, delay time=(0.03038x24x3600)/2pi=418 秒~7 分钟。

salmonfish

你是对的。但是题中未给出这些条件。我假设了两点都在赤道上，且地球自转轴与地球到太阳的方向相垂直（春季）。最简单情况。 www.ddhw.com

GiveATry

www.ddhw.com The speed of the rotation of the earth is 1 revolution per day. 1 revolution = the perimeter of the earth = 2 Pi r r =6.4x103 km is the radius of the earth  => 1 revolution = 2 x 3.14 x 6.4x103 = 40192 km Therefore the speed of the earth is: t = (40192/ 24) km/hr=1675 km/hr = (1675/1.609) mile/3600 second = 0.2891 mile/sec www.ddhw.com 1 mile = 1.609 km; 1 hour = 3600 second. We are given that the distance between this two cities is 120 miles, so after T seconds the person on the west side (city A) will see the sunrise: T= 120 miles / 0.2891 mile/sec ~ 415.08 seconds ~ 6.9 mintes So the person on the east side (city B) will see the rising sun about 6.9 minutes sooner than the one on the west side.   www.ddhw.com