Question

A runner is jogging in a straight line at a
steady Vy= 8.6 km/hr. When the runner is
L= 8.3 km from the finish line, a bird begins
flying straight from the runner to the finish
line at vy= 34.4 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
finish
line
What cumulative distance does the bird
travel? Even though the bird is a dodo, as-
sume 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.

Answer 1

Answer:

13.28 km

Explanation:

The bird flies from the runner, to the finish line, and back to the runner.  We can write two equations for the distance it travels:

d = 8.3 km + 8.3 km − 8.6 km/hr × t

d = 34.4 km/hr × t

Solve for t in the second equation and substitute into the first:

t = d / 34.4

d = 8.3 + 8.3 − 8.6 (d / 34.4)

d = 16.6 − 0.25 d

1.25 d = 16.6

d = 13.28

The bird flies a cumulative distance of 13.28 km.