A.) A runner is jogging at a steady 6.7 km/hr. When the runner is 3 km from the finish line, a bird begins flying from the runner to the finish line at 20.1 km/hr (3 times as fast as the runner). When the bird reaches the finish line, it turns around and flies back to the runner.How far does the bird travel? Even though the bird is a dodo, assume that it occupies only one point in space (a “zero” length bird) and that it can turn without loss of speed.
Answer in units of km
B.) After this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. The bird repeats the back and forth trips until the runner reaches the finish line.
How far does the bird travel from the be- ginning (including the distance traveled to the first encounter)?
Answer in units of km
To solve both questions, we need to consider the relative speeds and distances between the runner and the bird.
A.) To find how far the bird traveled to the finish line, we can calculate the time it takes for the bird to reach the finish line from the initial distance of 3 km.
The runner's speed is 6.7 km/hr, and the bird's speed is 20.1 km/hr (3 times the runner's speed). The relative speed between the bird and the runner is the difference between their speeds: 20.1 km/hr - 6.7 km/hr = 13.4 km/hr.
The time it takes for the bird to reach the finish line is calculated by dividing the initial distance (3 km) by the relative speed (13.4 km/hr):
Time = Distance / Speed
Time = 3 km / 13.4 km/hr = 0.224 hrs (rounded to three decimal places)
Since the bird flies at a constant speed, the distance it travels can be found by multiplying the bird's speed by the time:
Distance = Speed x Time
Distance = 20.1 km/hr x 0.224 hrs = 4.504 km (rounded to three decimal places)
Therefore, the bird travels approximately 4.504 km to reach the finish line.
B.) To find the total distance the bird travels, including the distance traveled in each round trip, we need to consider the runner's progress.
Let's calculate the time it takes for the runner to reach the finish line using their speed of 6.7 km/hr:
Time = Distance / Speed
Time = 3 km / 6.7 km/hr = 0.448 hrs (rounded to three decimal places)
Since the bird will make the same round trip to the runner multiple times until the runner reaches the finish line, the total distance can be calculated by multiplying the bird's speed by the total time:
Distance = Speed x Time
Distance = 20.1 km/hr x 0.448 hrs = 9.0048 km (rounded to four decimal places)
Therefore, the total distance the bird travels from the beginning (including the first encounter) is approximately 9.0048 km.