A runner is jogging steadily at 7.7km/hr. When the runner is 3.6km from the finish line, a bird begins flying from the runner to the finish line at 23.1km/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? Assume that the bird occupies only one point in space and it can turn without loss of speed.
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 beginning (including the first encounter)?
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WHAT THE NOODLE?!!
where do the 2.4 in part A and the 2.6 in part B come from
To find the distance the bird travels, we need to consider each leg of its journey.
Let's first calculate the time it takes for the runner to reach the finish line. We can use the formula: distance = speed × time.
Given that the runner is jogging at 7.7 km/hr and the remaining distance to the finish line is 3.6 km, we can calculate the time it takes for the runner to reach the finish line as follows:
Time = distance / speed = 3.6 km / 7.7 km/hr ≈ 0.467 hrs.
Now, let's calculate the distance the bird travels on the first leg of the journey. Since the bird is flying at 23.1 km/hr, three times the speed of the runner, and the time for the first leg is 0.467 hrs, we can use the formula: distance = speed × time.
Distance = 23.1 km/hr × 0.467 hrs ≈ 10.782 km.
However, this distance only accounts for the first leg of the journey. The bird flies back and forth between the runner and the finish line until the runner reaches the finish line.
Since the bird flies at the same speed as before, it will cover the distance between the runner and the finish line twice for each round trip. With each round trip, the distance reduces by 3.6 km.
Considering that the runner is 3.6 km away from the finish line initially, it will take (3.6 km / 3.6 km = 1) round trips for the runner to reach the finish line. Therefore, the bird will make (1 - 1) = 0 round trips.
To summarize, the bird will travel a total distance of 10.782 km on the first leg, and 0 km on subsequent back and forth trips, for a total distance traveled of 10.782 km.
So, the bird will travel a total distance of 10.782 km from the beginning (including the first encounter).
(a) It takes the bird 3.6/23.1 = 0.1558 h to teach the finish line. The runner is then 2.4 km from the finish line. They meet again 1.8 km from the finish line, since the bird travels 3/4 of the 2.4 km and the man 1/4.
The total distance travelled by the bird is 3.6 + 1.8 = 5.4 km
(b) It takes the man 2.6/7.7 = 0.3377 h to reach the finish line. The bird travels three times as far in the same interval, back and forth. That would be 10.80 km