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 birdWhat 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.
the runner.
Can someone please walk me through this
To solve this problem, we need to determine the cumulative distance traveled by the bird from the moment it starts flying until it reaches the finish line. We know that the bird's speed is 6 times faster than that of the runner.
Step 1: Calculate the time it takes for the runner to reach the finish line.
Distance = Speed × Time
The distance remaining for the runner to reach the finish line is L = 4.4 km.
The runner's speed is vr = 8.2 km/hr.
Time = Distance / Speed
Time = 4.4 km / 8.2 km/hr
Time = 0.5366 hours
Since time cannot be negative, we will consider positive solutions only.
Step 2: Calculate the distance the bird travels.
The bird starts flying when the runner is 4.4 km away from the finish line, and it reaches the finish line when the runner does. We can calculate the distance the bird travels by multiplying its speed with the time it takes for the runner to reach the finish line.
Distance traveled by the bird = Speed of the bird × Time taken by the runner
Distance traveled by the bird = 49.2 km/hr × 0.5366 hours
Distance traveled by the bird = 26.4312 km
Therefore, the cumulative distance traveled by the bird is approximately 26.4312 km.