How Does Earth's Longitude Affect Free Fall Equations?

[Garunekk]

Homework Statement

Solve free fall from height h to the Earth´s surface in the place longitude φ. During solving, Consider gravitation acceleration as a constant for the whole trajectory, so g=constant. (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.
Result should be y(t)=(gωt^3cosφ)/3

Homework Equations

m(dv/dx)(dx/dt)=-2mωvsinφ
Fc=-2mωvsinφ
v=v0+gt
y=y0+v0t+1/2gt^2
ω=v/r

The Attempt at a Solution

Tried to make an differential equations, bude i can't get to my result.

 

[Asim Riaz]

I think to solve this kind of problem, it is better to use projectile motion equations. So, let's start by finding the initial velocity (v0) in x and y direction:v0x=0 (initial velocity in x-direction is zero)v0y=√2gh (initial velocity in y-direction)Now, we have to find the angular speed (ω):ω=v0/r (where r is the distance travelled by the object)Substituting the values:ω=√2gh/rNow, we can use the equation for position:y=y0+v0t+1/2gt^2Substituting the values:y=(gωt^3cosφ)/3