Explain how you could determine, given the following 3 pieces of information, (you need all 3 together not each one individually) the radius of the Earth.
1) Jakarta and Port Moresby, the capital of Paua New Guinea, are two cities on the equator.
2) A plane leaves from Port Moresby bound for Jakarta at a speed of 500 mi/hr and arrives there 5 hours later.
3) A student in Port Moresby turns on a baseball game that is being played in Jakarta and starts right at the time of sunset in Port Moresby. The game finishes 3 hours later (an extra inning affair). The announcer comments at the end of the game that the Sun is just setting in Jakarta.
To determine the radius of the Earth using the given information, we can consider the following steps:
Step 1: Calculate the distance traveled by the plane.
Since the plane is traveling at a speed of 500 mi/hr for 5 hours, the total distance traveled would be:
Distance = Speed x Time
Distance = 500 mi/hr * 5 hr
Distance = 2500 miles
Step 2: Determine the time difference in sunset between Port Moresby and Jakarta.
As per the information provided, the baseball game in Jakarta finishes 3 hours after the sunset in Port Moresby. Since the game ends with the sunset in Jakarta, it means that the sunset in Jakarta occurred 3 hours later than in Port Moresby.
Step 3: Calculate the difference in longitude between Jakarta and Port Moresby.
To determine the time difference in sunset, we need to consider the difference in longitude between the two cities. Jakarta is on the western side of the Earth, while Port Moresby is on the eastern side. Since Earth rotates from west to east, the rotation results in the difference in time.
The Earth makes a complete rotation of 360 degrees in 24 hours. Therefore, each degree of longitude corresponds to one hour of time difference.
To find the difference in longitude between Jakarta and Port Moresby, we need to know their respective longitudes. Unfortunately, the given information does not provide the longitudes of the two cities. Therefore, without the longitude information, we cannot complete the calculation to determine the radius of the Earth accurately.
In conclusion, although we have three pieces of information, we lack the necessary longitude data to calculate the radius of the Earth accurately in this scenario.