Canadian geese migrate essentially along a north-south direction for well over a

Question

Canadian geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. If one such bird is flying at 100 km/h relative to the air, but there is a 30.0km/h wind blowing from west to east.

A.) At what angle relative to the north-south direction should this bird head so that it will be traveling directly southward relative to the ground?

B.) How long will it take the bird to cover a ground distance of 450km from north to south? (Note: Even on cloudy nights, many birds can navigate using the earth's magnetic field to fix the north-south direction.)

Please show work and how you knew what angle to use in either the cos or sin. I am having trouble understanding the concept.

Explanation / Answer

x direction = 0

so

100*sin(theta) - 30 = 0

theta= arcsin(30/100)= 17.46 degrees

b) v = d/t

t = d/v = 450/(100*cos(17.46 degrees))= 4.72 hours

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