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anonymous
 4 years ago
A runner is jogging at a steady 8.4 km/hr.
When the runner is 2.6 km from the finish
line, a bird begins flying from the runner to
the finish line at 42 km/hr (5 times as fast
as the runner). When the bird reaches the
finish line, it turns around and flies back to
the runner.
L
vb
vr
finish
line
How far does the bird travel? Even though
the bird is a dodo, assume that it occupies
only one point in space (a “zero” length bird)
and that it can turn without loss of speed.
Answer in units of km
anonymous
 4 years ago
A runner is jogging at a steady 8.4 km/hr. When the runner is 2.6 km from the finish line, a bird begins flying from the runner to the finish line at 42 km/hr (5 times as fast as the runner). When the bird reaches the finish line, it turns around and flies back to the runner. L vb vr finish line How far does the bird travel? Even though the bird is a dodo, assume that it occupies only one point in space (a “zero” length bird) and that it can turn without loss of speed. Answer in units of km

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Flight time of bird to finish line FL = 2.6/42 =(approx) .06hr Distance runner travels during time period = .06(8.4) = .52km Distance of runner to FL = 2.6.52 = 2.08km Net closing speed between runner and bird = 8.4km +42 km = 50.4km Time for runner and bird to meet 2.6/50.4 = (approx) .05hr Distance covered by runner (.05)8.4 = (approx) .43 km Distance covered by bird to runner (.05)(42) = (approx) 2.1km 2.1 + 2.6 = 4.7km (its not correct) :( What am I doing wrong?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.2The first piece is right of course, the bird first flies 2.6 km. I also agree that runner covers 0.52 km in that time. Start the clock again at that moment with t = 0. Write down the equations of motion now for runner and bird and solve them carefully. Runner's position, r(t) = (2.6  0.52) + 8.4t Bird's position, b(t) = 42t Now find out for what t: r(t) = b(t) and then use that to calculate the length of the bird's second leg of flight.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i understand what your saying (and sorry my internet connection seems to be troubled) 2.08 + 8.4t = 42t  8.4t = 8.4 2.08/33.6=33.6t/33.6 = .06 * Birds velocity (42) = 2.6 doesnt seem correct.

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.2Careful: 2.08 + 8.4t = 42t ... yes. But now... 2.08 = 50.4t => t = 0.04127 hours Hence the distance the bird covers in the second leg is:

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh goodness.... 1.68 + 2.6 = 4.28

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.2I get (distance of 2nd leg) = 0.0413 hours * 42 km/hr = 1.73 km

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yes. Apparently my finger slipped hen typing into the calculator. Thank you again.
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