005 (part 1 of 2) 10.0 points A runner is jogging in a straight line at a

steady vr= 8.5 km/hr. When the runner is

L=6.4 km from the finish line, a bird begins

flying straight from the runner to the finish

line at vý= 17 km/hr (2 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, 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

7.53 km

Explanation:

We at given;

Speed of runner; v_r = 8.5 km/hr

Speed of bird; v_y = 17 km/hr

L = 6.4 km

We know that; time = distance/speed.

We are told that the bird starts from 6.4 km from the start and that it flies back to meet the runner after it reaches the finish line. If the total distance back to the runner is x, it means bird distance is 6.4 + (6.4 - x) = 12.8 - x

Thus;

Time of bird(t_y) = (12.8 - x)/17

Thus,

Time of runner(t_r) = x/8.5 hr

To find x, we have to equate the times of the runner and the bird.

Thus;

x/8.5 = (12.8 - x)/17

Multiply both sides by 17 to get;

2x = 12.8 - x

2x + x = 12.8

3x = 12.8

x = 12.8/3

x = 4.27 km

Thus, cumulative distance traveled by bird is; 12.8 - 4.27 = 7.53 km

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