A drone can fly motorlessly during the day because there is enough thermal energy to power it. As a result, it loses an average of 2/3 km of altitude. At night it gains another 7/12 km of altitude with the help of its engine.
When will it land on earth again if it climbs to 10 km on the morning of May 1, 2020 and continues flying as described above?
The drone will rise to a height of 10 km on the morning of May 1, 2020 and will fly motorlessly. Over time, it will lose 2/3 km (= 8/12 km) of altitude. At night, it will gain an altitude of 7/12 km with the help of its engine.
Every 24 hours, it loses 1/12 km (- 8/12 km + 7/12 km) of altitude. By the morning of May 2, it will have lost 1/12 km of altitude. This process continues.
As soon as the drone has lost so much altitude that it is 2/3 km (=8/12 km) from earth at daybreak, it will land on earth in the evening of the corresponding day.
To calculate the number of day/night flights until the drone is at an altitude of 2/3 km (=8/12 km), we will use the following formula:
2/3 km (= 8/12 km):
8/12 km = 10 km - (1/12 km * x)
x = 112
As you can see, it takes 112 day/night periods before the drone is at an altitude of 2/3 km (= 8/12 km). On the morning of August 21, it will start sinking by exactly this height over the course of the day. This means it will land on earth on the evening of August 21 after 112.5 days.