Final answer:
The bird flies a cumulative distance of approximately 9.461 kilometers before the runner reaches the finish line.
Step-by-step explanation:
The question involves calculating the cumulative distance traveled by a bird while a runner is jogging towards a finish line. Given that the bird's velocity is twice that of the runner's (7 km/h for the bird and 3.5 km/h for the runner) and that the bird starts flying when the runner is 7.1km from the finish line, we can calculate the distance the bird travels until the runner reaches the finish line.
Firstly, we determine the time it takes for the bird to reach the finish line:
Time = Distance / Speed = 7.1 km / 7 km/h = 1.0167 hours (approximately).
During this time, the runner covers a distance of: Runner's distance = Runner's speed * Time = 3.5 km/h * 1.0167 hours = 3.558 km (approximately), leaving the runner 7.1 km - 3.558 km = 3.542 km from the finish line.
Next, we find how long the bird flies back to meet the runner. The relative speed towards each other is the sum of their velocities: Relative speed = Runner's speed + Bird's speed = 3.5 km/h + 7 km/h = 10.5 km/h.
The time for the bird to meet the runner is: Meeting time = Remaining distance / Relative speed = 3.542 km / 10.5 km/h = 0.3373 hours (approximately).
The distance the bird flies back to the runner: Bird's distance back = Bird's speed * Meeting time = 7 km/h * 0.3373 hours = 2.361 km (approximately).
Add the two distances the bird travels to get the cumulative distance:Cumulative distance = Distance to finish line + Distance back to runner = 7.1 km + 2.361 km = 9.461 km (approximately).