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I am absolutely stumped regarding this questions. Could someone please assist me? I would be extremely grateful.

A runner is jogging at a steady v = 8.4 km/hr. When the runner is L = 4.9 km from the finish line, a bird begins flying from the runner to the finish line at V = 16.8 km/hr (2 times as fast as the runner). When the bird reaches the finish line, it turns around and flies back to the runner. We will assume that the bird occupies only one point in space, ie., a zero length bird.

How far does the bird travel? Answer in units of km.

ALSO:

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? (ie include the distance traveled to the first encounter) Answer in units of km.

2007-08-24 03:54:04 · 3 answers · asked by sg88 1 in Science & Mathematics Physics

3 answers

At first glance, it looks like you have to add up an infinite number of vanishingly small distances. But there's a much easier way.

1. Calculate the amount of time it takes for the runner to reach the finish line (from the time of the first bird encounter). This is just: t = distance/speed.

2. The bird is flying at a constant speed during all that time (it changes direction instantaneously). So, just calculate how far a bird traveling at speed V can travel in time t.

2007-08-24 04:43:18 · answer #1 · answered by RickB 7 · 1 0

Let them meet at a distance y from the start.

Time for the runner to travel y km =y /8.4 hour.

During this time the bird travels a distance of [y /8.4] x 16.8 / = 2y


2y = 4.9 + {4.9 - y]

2y = 9 -y

3y =9
y = 3 km.

the distance traveled by bird is 2y = 6km

or 9- y = 6km.

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Let them meet finally at the finish line after a time t

Time for the runner to travel 4.9 km = 4.9 / u.

where u is the speed of the runner.

During this time the bird travels a distance of [4.9 / u.] * v where v is the speed of the bird.

Since v/u = 2.

The distance traveled by bird is 2 x 4.9 = 9 km.

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2007-08-24 06:00:39 · answer #2 · answered by Pearlsawme 7 · 0 0

The runner will cover the distance 4.9 km.
The bird files twice as fast and will cover distanse twice as large in the same time.

Answer: 2*4.9km = 9.8 km

2007-08-24 04:43:20 · answer #3 · answered by Alexander 6 · 0 0

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