Does vertical coriolis force affect motions of projectiles?

Question

If an object is projected towards east or west from the equator, we get the coriolis force to be vertical. If this projectile, say, miss its target from below, can this be attributed to the coriolis force?

Answer 1

Yes, the Coriolis force must be included in the equations of motion if you want to take the surface of the Earth as your reference frame and predict trajectories. This is because the Coriolis force, like all psuedoforces, is an expression of the velocity of the projectile, with a coordinate transformation into the non-inertial frame of the surface of the Earth. Exactly as you need initial velocity and real forces to predict the motion of projectiles in an inertial frame, you need initial velocity, real forces, and pseudoforces to predict the motion of projectiles in a non-inertial frame.

Projectiles launched west-to-east tangent to the surface of the Earth will seem to accelerate upwards, then (if they attain a positive vertical velocity) westwards under the Coriolis force.

To understand what's going on, get rid of gravity and consider the problem in two dimensions. Alice is on a rotating platform. She tosses a ball to Bob, standing on the ground a few meters away, when he is tangent to the rotation of the platform. Alice watches Bob traverse a big arc like the sun going across the sky, while the ball homes in on Bob on an intercept course, propelled by a psuedoforce. Bob, of course, watches Bob stand still where he started, while the ball goes in a straight line from where Alice started to where Bob started.

(I made the below illustration in MSPaint, so don't expect the curves to be quite right.)