A satellite is orbiting Earth in a circular orbit at an altitude of $500$ km above the surface. The satellite deploys a payload that moves radially outward from the satellite's cabin with a relative velocity of $100\frac{m}{s}.$ The latitude of deployment is $30.$

Assume:

Earth's radius: $R_E=6,371km,$

Earth's angular velocity: $=7\mathrm{.}292{10}^{-5}ra\frac{d}{s},$

Mass of the payload: $100$ kg $.$

a$)$ The Coriolis force acting on the payload immediately after deployment.

b$)$ The direction of the Coriolis force.

$(2$ Marks$)$