A runner is jogging in a straight line at a steady vr= 2.2 km/hr. When the runner is L= 4 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 6.6 km/hr (3 times as fast as the runner). When the bird reaches the finishline, it turns around and flies directly back to the runner.
Q1: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.
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)?I CANT UNDERSTAND please someone explain to me thank you!
Q1: The distance the bird travels is equal to the distance between the runner and the finish line, which is 4 km. Since the bird is flying at a speed of 6.6 km/hr, it will take the bird (4 km / 6.6 km/hr) = 0.606 hours to reach the finish line.
Q2: After the first encounter, the bird turns around and flies back to the finish line, which is again a distance of 4 km. Then, it turns around and flies back to the runner. The bird repeats this process until the runner reaches the finish line. Since the runner is traveling at a speed of 2.2 km/hr, it will take the runner (4 km / 2.2 km/hr) = 1.82 hours to reach the finish line.
During this time, the bird will go back and forth multiple times. In each round trip, the bird covers a distance of 4 km. So, for the bird to cover the same distance as the runner, it needs to make (4 km / 4 km) = 1 round trip. However, since the bird is flying three times as fast as the runner, it will actually make (1 round trip * 3 times) = 3 trips during the time it takes for the runner to reach the finish line.
Therefore, the total distance traveled by the bird from the beginning is equal to the distance covered during the first encounter (4 km) plus the distance covered in the subsequent round trips (3 trips * 4 km) = 4 km + (3 * 4 km) = 16 km.
Sure! Let's break down the problem step by step to understand what's happening.
In the given scenario, we have a runner jogging at a speed of 2.2 km/hr. The finish line is 4 km away from the runner.
1. Cumulative Distance the Bird Travels:
The bird is initially at the same location as the runner (since it starts from the runner). It flies straight to the finish line at a speed of 6.6 km/hr (3 times the speed of the runner). To find the time it takes for the bird to reach the finish line, we can use the formula:
Time = Distance / Speed.
In this case, the distance is 4 km, and the speed is 6.6 km/hr. So, Time = 4 km / 6.6 km/hr = 0.606 hours.
Now, we want to find the distance covered by the bird. Since the bird flies directly from the runner to the finish line, its distance travelled will be the same as the distance between the runner and the finish line. So, the bird travels 4 km.
2. Distance the Bird Travels in All Trips:
After the first encounter, the bird turns around and flies from the finish line back toward the runner. Since its speed is the same (6.6 km/hr), it will take the bird the same amount of time (0.606 hours) to travel back to the runner. In this time, the runner has advanced 2.2 km (his speed multiplied by the time).
The bird then repeats this back-and-forth trip until the runner reaches the finish line. Each time, the distance covered by the runner will remain the same (2.2 km), and the bird will cover double that distance (4.4 km) because it has to fly both ways. So, for every trip, the bird travels 4.4 km.
To find the total distance covered by the bird, we need to add up the distances covered in each trip. Since the runner covers a total distance of 4 km before reaching the finish line, there will be a total of 4 km / 2.2 km = 1.818 trips. As the bird covers 4.4 km per trip, the total distance covered by the bird will be 1.818 trips x 4.4 km/trip = 7.9988 km.
So, the cumulative distance the bird travels from the beginning (including the distance traveled to the first encounter) is approximately 7.9988 km.
I hope this explanation helps! If you have any further questions, feel free to ask.
What cumulative distance does the bird
A runner is jogging in a straight line at a
steady vr= 8.2 km/hr. When the runner is
L= 4.4 km from the finish line, a bird begins
flying straight from the runner to the finish
line at vb= 49.2 km/hr (6 times as fast as
the runner). When the bird reaches the finishtravel? 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 line, it turns around and flies directly back to
the runner.
speed.
Answer in units of km.
whoops, in the first part:
so how long did the bird fly? t+T
4/6.6 + 2/6.6 = 6/6.6 hours
and how far did it go?
(6/6.6)*6.6 = 6 km
let vr = 2.2
The bird flies 4 km to the line: t = 4/(3*2.2) hour
in that time the runner goes 2.2 t = (4/3)km
so the runner is at 4 - 4/3 = 8/3 km from finish when the bird is at finish
now the bird starts back and the runner continues for time T when hey meet
so
(8/3 km) = (runnerspeed*T +bird speed*T
8/3 = T (2.2 + 3*2.2) = 4*2.2 T
T = 2/6.6 Hr = 1/3.3 hr
so how long did the bird fly? t+T
4/6.6 + 2/6.6 = 6/6.6 hours
and how far did it go?
6.6 + 6/6.6*6.6 = 2*6.6 = 13.2km
Part 2 is really easy
it takes the runner 4 / 2.2 hours to finish
the bird flies that whole time so flies
6.6 *4/2.2 = 3*4 = 12 km