Physics

A runner is jogging in a straight line at a steady vr= 2.2 km/hr. When the runner is L= 4 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 6.6 km/hr (3 times as fast as the runner). When the bird reaches the finishline, it turns around and flies directly back to the runner.
Q1: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.
Q2: 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)?I CANT UNDERSTAND please someone explain to me thank you!

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  1. let vr = 2.2
    The bird flies 4 km to the line: t = 4/(3*2.2) hour
    in that time the runner goes 2.2 t = (4/3)km
    so the runner is at 4 - 4/3 = 8/3 km from finish when the bird is at finish
    now the bird starts back and the runner continues for time T when hey meet
    so
    (8/3 km) = (runnerspeed*T +bird speed*T
    8/3 = T (2.2 + 3*2.2) = 4*2.2 T
    T = 2/6.6 Hr = 1/3.3 hr
    so how long did the bird fly? t+T
    4/6.6 + 2/6.6 = 6/6.6 hours
    and how far did it go?
    6.6 + 6/6.6*6.6 = 2*6.6 = 13.2km

    Part 2 is really easy
    it takes the runner 4 / 2.2 hours to finish
    the bird flies that whole time so flies
    6.6 *4/2.2 = 3*4 = 12 km

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  2. whoops, in the first part:
    so how long did the bird fly? t+T
    4/6.6 + 2/6.6 = 6/6.6 hours
    and how far did it go?
    (6/6.6)*6.6 = 6 km

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  3. What cumulative distance does the bird
    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 bird reaches the finishtravel? 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 line, it turns around and flies directly back to
    the runner.

    speed.
    Answer in units of km.

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