A runner is jogging in a straight line at a
steady vr= 3.1 km/hr. When the runner is
L= 6.1 km from the finish line, a bird begins
flying straight from the runner to the finish
line at vb= 18.6 km/hr (6 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.
My teacher tried giving me a formula and explaining but it still made no sense.
the bird flies for as long as it takes the runner to finish
(6.1 km / 3.1 km/hr) * 18.6 km/hr = ?
I need help asap please
i dont really see how that works out but thank you so much
I will try to make it clear.
The runner takes a certain time to finish. (6.1 km / 3.1 km/hr) which is distance over runner speed.
The bird is flying at 18.6 km/hr for exactly that length of time.
To solve this problem, let's break it down into smaller steps.
Step 1: Calculate the time it takes for the runner to reach the finish line.
We can use the formula Time = Distance / Speed. The runner's speed is 3.1 km/hr, and the distance to the finish line is 6.1 km. So, the time it takes for the runner to reach the finish line is 6.1 km / 3.1 km/hr = 1.97 hours.
Step 2: Calculate the distance the bird travels toward the finish line.
Since the bird flies at 18.6 km/hr (6 times faster than the runner), we can calculate the distance it travels by multiplying its speed by the time it takes for the runner to reach the finish line. The distance the bird travels is 18.6 km/hr * 1.97 hours = 36.6 km.
Step 3: Calculate the time it takes for the bird to fly back to the runner.
Since the bird is flying back to the runner, the distances covered will be the same. We can use the formula Time = Distance / Speed, where the distance is 36.6 km (from step 2) and the speed is 18.6 km/hr. The time it takes for the bird to fly back to the runner is 36.6 km / 18.6 km/hr = 1.97 hours (which is the same as in step 1).
Step 4: Calculate the cumulative distance the bird travels.
The cumulative distance is the sum of the distances traveled toward the finish line and back to the runner. So, the cumulative distance the bird travels is 36.6 km + 36.6 km = 73.2 km.
Answer: The cumulative distance the bird travels is 73.2 km.