Question

A geostationary satellite S is stationed above a point P on the equator. A particle is fired from S directly towards P

• A. With respect to the axis of rotation of the earth, P and S have the same angular velocity but different linear velocities
• B. The particle will hit P
• C. The particle will hit the equator east of P
• D. The particle will hit the equator west of p

Answer 1

Answer: (A), (C)

With respect to the axis of rotation of the earth, P and S have the same angular velocity but different linear velocities
The particle will hit the equator east of P

Since the satellite is geostationary, an observer on equator does not see the satellite revolving around earth. This means the relative angular velocity is zero. Thus they have same angular velocity.
The linear velocity of each of point P and S is given by angular velocity times the distance of them from center of earth, which is different for both.

As an object is thrown towards point P, as it takes time to reach the surface, due to the linear velocity perpendicular to the direction of projection, due to the initial angular velocity(west to east) it had, it hits the ground to the East of point P.