Q1: A runner is jogging in a straight line at a steady vr= 6.8 km/hr. When the runner is L= 2.4 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 13.6 km/hr (2 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.
Q2: 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 beginning (including the distance traveled to the first encounter)? Answer in units of km.
Q1 the bird flies twice as fast as the runner for the same amount of time
... so the bird travels twice as far as the runner
Q2 doesn't seem to make sense
Yo Scott, you got Q1 wrong and I still need help on Q2, please help me Scott!!!!!😖 😫 😩
To find the cumulative distance traveled by the bird in both scenarios, we need to break down each scenario and calculate the distance traveled in each interval.
Q1:
In this scenario, the bird starts flying when the runner is 2.4 km away from the finish line. The bird flies straight to the finish line at a speed of 13.6 km/hr, which is 2 times faster than the runner.
To find the time it takes for the bird to reach the finish line, we divide the distance (2.4 km) by the bird's speed (13.6 km/hr):
Time = Distance / Speed = 2.4 km / 13.6 km/hr = 0.1765 hr
Since the bird is flying straight without any loss of speed, it immediately turns around and starts flying back to the runner. The distance traveled by the bird is the same as the distance from the finish line to the runner, which is also 2.4 km.
Therefore, in this scenario, the cumulative distance traveled by the bird is twice the distance from the finish line to the runner:
Cumulative distance = 2 * 2.4 km = 4.8 km
So the bird travels a cumulative distance of 4.8 km in this scenario.
Q2:
In this scenario, the bird repeats the back and forth trips until the runner reaches the finish line. Let's break it down step by step:
1. The bird starts flying from the beginning (start line) to the runner. The initial distance from the start to the runner is 2.4 km.
2. It then turns around and flies back from the runner to the finish line. The distance from the runner to the finish line is also 2.4 km.
3. The bird again turns around and flies from the finish line back to the runner, covering another 2.4 km.
4. This pattern continues until the runner reaches the finish line.
In each back and forth trip, the bird covers a total distance of 2.4 km (from the runner to the finish line and back). Since the runner is already 2.4 km away from the finish line, the total distance covered by the bird from the beginning is:
Cumulative distance = 2.4 km + 2.4 km + 2.4 km + ... (repeated until the runner reaches the finish line)
To calculate the total cumulative distance, we need to know how many times the bird needs to fly back and forth. This can be obtained by dividing the total distance the runner needs to cover (2.4 km) by the distance covered by the bird in one back and forth trip (2.4 km).
Total number of trips = Total distance / Distance per trip = 2.4 km / 2.4 km = 1
Since the total number of trips is 1, the cumulative distance traveled by the bird from the beginning is:
Cumulative distance = Total number of trips * Distance per trip = 1 * 2.4 km = 2.4 km
So the bird travels a cumulative distance of 2.4 km from the beginning (including the distance traveled to the first encounter).
To summarize:
Q1: The bird travels a cumulative distance of 4.8 km in this scenario.
Q2: The bird travels a cumulative distance of 2.4 km from the beginning in this scenario.