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
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
Stacey Warren - Expert brainly.com
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Flight 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?
The 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.