A communications satellite is in an orbit that is 3.1 multiplied by 107 m directly above the equator. Consider the moment when the satellite is located midway between Quito, Equador, and Belem, Brazil; two cities almost on the equator that are separated by a distance of 3.6 multiplied by 106 m. Find the time it takes for a telephone call to go by the way of satellite between these cities. Ignore the curvature of the earth.

I assume by 107 you mean 10^7, so the satellite is at an altitude of 31000 km.

If we ignore the curvature of the earth, and consider it a plane, then we have an isosceles triangle of height 3.1x10^7m, and a base of 3.1x10^6m, similar to a triangle of base 1, height 10. So, the distance traveled is 3.1x10^6 * sqrt(101) * 2 = 62.3x10^6m.

The speed of light is 3.0x10^8m/s

so, the call takes 6.23x10^7/3.0x10^8 = 2.07x10^-1 = 0.207s.

To find the time it takes for a telephone call to go by the way of satellite between Quito, Ecuador, and Belem, Brazil, we need to calculate the round trip time (RTT) of the signal.

Step 1: Calculate the distance traveled by the signal:
The signal needs to travel from Quito to the satellite, then from the satellite to Belem, and finally back to Quito. So, the total distance traveled by the signal is:
Distance traveled = 2 × (distance from Quito to the satellite) + distance from the satellite to Belem
= 2 × (3.1 × 10^7 m) + (3.6 × 10^6 m)
= 6.2 × 10^7 m + 3.6 × 10^6 m
= 6.56 × 10^7 m

Step 2: Calculate the time it takes for the signal to travel the distance:
To calculate the time it takes for the signal to travel the distance, we need to divide the distance traveled by the speed of light. The speed of light is approximately 3 × 10^8 m/s.

Time taken = Distance traveled / Speed of light
= (6.56 × 10^7 m) / (3 × 10^8 m/s)
≈ 0.22 seconds

Therefore, it takes approximately 0.22 seconds for a telephone call to go by the way of satellite between Quito, Ecuador, and Belem, Brazil.