Q.1 A runner is jogging in a straight line at a
steady vr= 4.2 km/hr. When the runner is
L= 2.1 km from the finish line, a bird begins
flying straight from the runner to the finish
line at vb= 21 km/hr (5 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.
To find the cumulative distance traveled by the bird, we need to break down the problem into smaller steps:
Step 1: Calculate the time it takes for the bird to reach the finish line.
To find the time, we use the formula: time = distance / speed.
In this case, the distance is L (2.1 km) and the speed of the bird, vb, is 21 km/hr.
So, the time taken by the bird to reach the finish line is: t1 = L / vb = 2.1 km / 21 km/hr = 0.1 hr.
Step 2: Calculate the time it takes for the bird to fly back from the finish line to the runner.
Since the bird turns around and flies directly back to the runner, the distance it needs to cover is also L (2.1 km).
The speed of the bird, vb, remains the same at 21 km/hr.
So, the time taken by the bird to fly back is: t2 = L / vb = 2.1 km / 21 km/hr = 0.1 hr.
Step 3: Calculate the cumulative distance traveled by the bird.
The bird travels two distances: one while flying to the finish line, and the other while flying back to the runner.
The distance covered in each leg is L (2.1 km), and the total time taken is t1 + t2 = 0.1 hr + 0.1 hr = 0.2 hr.
The cumulative distance traveled by the bird is therefore: cumulative distance = distance to the finish line + distance back to the runner = 2 * L = 2 * 2.1 km = 4.2 km.
So, the cumulative distance traveled by the bird is 4.2 km.