How Does Coriolis Force Affect Free Fall at the Equator?

[Garunekk]

Hi,
I would need some help with my homework. I am lost.

Solve free fall from height h to the Earth´s surface in the place with geographical width φ. During solving, omit addiction gravitational acceleration to the distance. (consider a homogeneous gravity field) and variables which are including angular speed ω consider for much less then variables including gt. Consider h=100m and
φ=0 degree.

The result should be y(t)=(gωt^3cosφ)/3. Bud I am not sure, how to get it. I am sure I have to use Coriolisi´s force. But as I said, I am lost.
Thank you for your help and sorry for my bad english.

 

[jbsteele]

The solution can be derived from the equation of motion for a free falling object in a homogeneous gravitational field,d2y/dt2 = -gwhere g is the gravitational acceleration and y is the vertical displacement of the object.By substituting in the angular speed (ω) and the geographic width (φ), we obtain the equationd2y/dt2 = -gωcosφIntegrating twice with respect to time yields the equationy(t) = -gt^2ωcosφ/2 + C1t + C2where C1 and C2 are constants of integration.Using initial conditions, namely that y(0) = h and dy/dt(0) = 0, we can solve for C1 and C2. This yields the solution y(t) = (gωt^3cosφ)/3 + h