Question

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

Answer 1

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?

Answer 2

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.

Answer 3

Make sense?

Answer 4

i 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.

Answer 5

Careful:
-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:

Answer 6

oh goodness.... 1.68 + 2.6 = 4.28

Answer 7

I get
(distance of 2nd leg) = 0.0413 hours * 42 km/hr = 1.73 km

Answer 8

Yes. Apparently my finger slipped hen typing into the calculator. Thank you again.

Answer 9

Sure