"Julia and Heiko are two enthusiastic caching sparrows. Therefore, when a new cache is published nearby, they both leave their nests immediately. The cache hiding place is located exactly on the midpoint of the line joining their two nests. Heiko lives to the east and Julia to the west of the hiding place.
In the absence of any wind, both can fly at a speed of 60 km/h . However, on this day, there is a strong wind from the east, blowing with a speed of 44 km/h. This causes Julia's arrival to be one minute later than Heiko, whom, by this time, is already on his way back to his nest which is located at N 52° 30.098 E 13° 22.547."
To solve this problem, we need to break it down into steps. Here's how you can find the location of the cache hiding place:
Step 1: Determine the distance between Julia's nest and the cache hiding place.
Since Julia's nest is located to the west of the hiding place, we know that the wind will affect her travel time. However, since the wind is blowing from the east, it will oppose her motion and slow her down. The formula to calculate the time traveled is:
Time = Distance / Speed
We want to find the distance, so we rearrange the formula:
Distance = Time * Speed
Given that the speed of Julia's flight is 60 km/h and the wind is blowing from the east with a speed of 44 km/h, we can calculate the time it takes for her to arrive one minute later than Heiko (who is not affected by the wind):
Time = 1 minute = 1/60 hour
Using this time, we can calculate the distance traveled by Julia:
Distance = (1/60) * (60 - 44)
Step 2: Determine the location of the cache hiding place.
Since the cache hiding place is located at the midpoint between Julia's and Heiko's nests, we need to find the coordinates of this midpoint.
To do this, we first need to know the coordinates of Heiko's nest, which are provided as N 52° 30.098 E 13° 22.547.
Next, we need to calculate the change in latitude and longitude caused by the distance traveled by Julia. We can assume that the latitude remains unchanged, and only the longitude is affected. One degree of longitude is approximately 111 km.
Change in longitude = Distance / 111
Given that the distance traveled by Julia is Distance (calculated in Step 1), we can calculate the change in longitude.
Change in longitude = Distance / 111
Finally, we can find the longitude of the cache hiding place by subtracting the change in longitude from Heiko's longitude.
Longitude of cache hiding place = Heiko's longitude - Change in longitude
The latitude of the cache hiding place remains the same as Heiko's latitude.
Putting it all together, you can now calculate the location of the cache hiding place.