Question

A runner is jogging in a straight line at a steady vr= 7 km/hr. When the runner is L= 7.6 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 28 km/hr (4 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.

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.

Answer 1

See answers below

Step-by-step explanation:

Rate of runner 7 km/hr

Bird = 28 km/ hr

TIME bird flies to finish line 7.6 km / 28 km/hr

the runner covers distance in this time :

7.6 / 28 * 7 km = 1.9 km

this leaves 7.6 - 1.9 km = 5.7 km to the finish

..... the bird turns around

now the two have a closing speed of 28 + 7 = 35 km/hr to cover

this 5.7 remaining km

time to meet = 5.7 km / 35 km/hr = .16285 hr

so the bird flies at 28 km/ hr for this remaining time

= 4.56 km added to the original 7.6 km before turning around = 12.16 km

Total time for the runner to finish 7.6 km / 7 km/hr = 1.086 hr

the bird is flying at 28 km/hr for this entire time = 30. 4 km