A runner is jogging in a straight line at a steady vr =5 km/hr.When the runner is L= 6.2 km from the finish line, a bird begins flying straight from the runner to the finish line at vb=15 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.
What cumulative distance does the bird travel? Even though the bird is a dodo, assume 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.
Can anyone help me with this problem? I've tried it multiple times and can't get the answer.
To solve this problem, we need to understand the relative motion between the runner and the bird.
Let's consider the time it takes for the bird to reach the finish line. Since the bird is flying at three times the speed of the runner, it will cover the distance of L=6.2 km in L/vb = 6.2/15 = 0.4133 hours.
During this time, the runner will still be jogging at a speed of vr=5 km/hr. Therefore, the distance covered by the runner during this time is (vr x time) = 5 x 0.4133 = 2.0666 km.
Now, the bird turns around and flies directly back to the runner. We already know that it took 0.4133 hours for the bird to travel from the runner to the finish line. It will take the same amount of time for the bird to return.
During this time, the runner is still jogging at a speed of 5 km/hr. Therefore, the distance covered by the runner during the bird's return journey is also (vr x time) = 5 x 0.4133 = 2.0666 km.
The cumulative distance traveled by the bird is the sum of the distances it covered while going to the finish line and coming back.
Cumulative Distance = Distance to Finish Line + Distance from Finish Line
Cumulative Distance = 6.2 km + 6.2 km = 12.4 km.
Therefore, the bird travels a cumulative distance of 12.4 km.