It is a well-known fact that homing pigeons fly faster over land than over water. Assume that they fly at 10 metres per second over land, and only 8 metres per second over water.
A pigeon is located at the edge of a straight river bank, 500 metres wide, and must fly to its nest, located 1 300 metres away on the opposite bank of the river
5.1 Show the time taken for the journey home
5.2 Describe the path that would minimise the pigeon’s flying time
To determine the time taken for the journey home, we need to calculate the time taken to cross the river and the time taken to fly over land.
5.1 Time taken to cross the river:
The pigeon flies slower over water, at a speed of 8 meters per second. The width of the river is 500 meters. To calculate the time taken to cross the river, we divide the width of the river by the speed of the pigeon over water:
Time taken to cross the river = Width of the river / Speed over water
Time taken to cross the river = 500 meters / 8 meters per second
Time taken to cross the river = 62.5 seconds
5.2 Path that minimizes flying time:
To minimize the flying time, the pigeon should choose the path that minimizes the time taken to cross the river and the time taken to fly over land.
Since the pigeon flies faster over land than over water, it is more efficient to spend less time flying over water and more time flying over land. Therefore, the pigeon should choose the path that results in the shortest distance over water.
In this scenario, the shortest distance over water would be a straight line path from the starting point on one riverbank to the endpoint on the opposite riverbank. This path would minimize the time taken to cross the river.
Once the pigeon has crossed the river, it can fly directly to its nest, located 1,300 meters away over land. Since the pigeon flies at a speed of 10 meters per second over land, we can calculate the time taken to fly over land by dividing the distance by the speed:
Time taken to fly over land = Distance / Speed over land
Time taken to fly over land = 1,300 meters / 10 meters per second
Time taken to fly over land = 130 seconds
To determine the total time taken for the journey home, we sum the time taken to cross the river and the time taken to fly over land:
Total time taken for the journey home = Time taken to cross the river + Time taken to fly over land
Total time taken for the journey home = 62.5 seconds + 130 seconds
Total time taken for the journey home = 192.5 seconds
Therefore, the time taken for the pigeon to complete the journey home is 192.5 seconds.