A runner is jogging in a straight line at a steady vr= 5.3 km/hr. When the runner is L= 7 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 15.9 km/hr (3 times as fast as the runner). When the bird reaches the finish line, it turns around and flies directly back to the runner. L vb vr finish line What cumulative distance does the bird travel? Even though the bird is a dodo, as�sume that it occupies only one point in space (a “zero” length bird), travels in a straight line, and that it can turn without loss of speed. Answer in units of km
To find the cumulative distance the bird travels, we need to analyze its movements. Let's break it down step by step.
1. Initially, the runner is L = 7 km from the finish line, and the bird is at the same position as the runner.
2. As the runner continues to jog towards the finish line at a speed of vr = 5.3 km/hr, the bird starts flying towards the finish line at a speed of vb = 15.9 km/hr.
3. Since the bird flies 3 times as fast as the runner, it will catch up with the runner. The time it takes for the bird to reach the finish line can be calculated using the formula:
Time = Distance / Speed
The distance between the runner and the finish line is L = 7 km. The speed of the bird is vb = 15.9 km/hr.
Therefore, the time taken by the bird to reach the finish line is:
Time = 7 km / 15.9 km/hr = 0.439
4. After reaching the finish line, the bird immediately turns around and flies back towards the runner without loss of speed. The distance between the finish line and the runner is also L = 7 km.
5. The bird's speed remains constant at vb = 15.9 km/hr for the return journey as well. Therefore, the time taken by the bird to travel back to the runner is the same as the time taken to reach the finish line, which is 0.439 hours.
6. The cumulative distance traveled by the bird is the sum of the distances covered during its outward and return journeys. Since the bird's speed remains constant, we can use the formula:
Distance = Speed × Time
Distance = 15.9 km/hr × 0.439 hr = 6.981 km (rounded to 3 decimal places)
Hence, the cumulative distance traveled by the bird is approximately 6.981 km.