A birdwatcher observes an eagle in flight on a windy day. As the eagle flies eas
ID: 1414582 • Letter: A
Question
A birdwatcher observes an eagle in flight on a windy day. As the eagle flies east with the wind, the birdwatcher observes it traveling 361 m in 29.3 s. The eagle turns around and flies west into the wind, taking 36.4 s to travel the same distance of 361 m. Assuming the eagle's velocity relative to the air and the wind's velocity relative to the birdwatcher are both constant, what must be the eastward velocity of the wind? If the eagle then attempts to fly northward, what velocity relative to the birdwatcher will the eagle have? Give the direction in degrees east of north.
Explanation / Answer
Let the velocity of wind be vw .
Now while travelling east,
vb + vw = 361/29.3
vb + vw = 12.32
While travelling west,
vb - vw = 361/36.4
vb - vw = 9.92
Solving the two eq,
vb = 11.12 m/s
vw = 1.2 m/s
Eastward velocity of the wind, Vw = 1.2 m/s
If Fluing Northward,
V = sqrt(vb^2 + vy^2)
V = sqrt(11.12^2 + 1.2^2)
V = 11.18 m/s
Direction = tan^-1(11.12/1.2)
Direction = 83.84 o
Direction = 6.16o east of North