How Is the Coriolis Force Applied in Calculating Free Fall?

[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.

I tried to use formulas for free fall

v=v0+gt
y=y0+v0t+1/2gt^2

And use Coriolis force Fc=-2mωvsinφ
And acceleration ac=-2ωv

I tried also create a differential equation as a

m (dv/dx)(dx/dt)=-2mωvsinφ, where dx/dt=v

But no matter what, I still couldn´t get to my result.

Thank you for your help.

 

[AvroArrow]

You can use the following equations to solve for y(t):v=v0+gty=y0+v0t+1/2gt^2For the given conditions (h=100m, φ=0 degree), we can set:v0 = 0 m/s (since you are starting from rest)y0 = 100 m (since h is equal to 100m)Substituting these values into the equations above, we have:v=gty=100+1/2gt^2 Now, since you are considering a homogeneous gravity field, we can replace g with (gωtcosφ) and obtain:v=(gωtcosφ)y=100+(1/2)(gωtcosφ)^2 Simplifying, we get:y(t)=(gωt^3cosφ)/3which is the desired result.