Math & Science Home  Proficiency Tests  Mathematical Thinking in Physics  Aeronauts 2000 

Falling EastwardProblem: Solution: and is directed eastward. The term v is the velocity of the falling test object as a function of time. If the eastward deflection is assumed sufficiently small compared to h, we may approximate v and h as Substituting 2. into 1. gives for the Coriolis acceleration
Integrating once give the eastward velocity as a function of time
Integrating a second time gives the required deflection
Using 3., t^{3} = (2h/g)^{3/2}, so that for the entire fall from height h,
Let us now assume that the initial height h = 100 m, and l = 42 deg. With = 7.27 x 10^{7} /sec, we find that at the moment of impact, t =
4.52 sec
v = 44.3 m/sec v_{E} = 1.08 x 10^{4} m/sec x_{E} = 1.63 x 10^{4} m = .16 mm Comparing v_{E} and v, we also see that the deviation of the velocity from the vertical is arctan
(1.08 x 10^{4}/44.3) = 1.4 x 10^{4} deg.
With h = 1000 m, l = 42 deg, we find t =
14.3 sec
v = 140 m/sec v_{E} = 1.08 x 10^{3} m/sec x_{E} = 5.16 x 10^{3} m = 5.16 mm with arctan (1.08 x 10^{3}/140) = 4.4 x 10^{4} deg.


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