Question

A ball is thrown horizontally and another ball is just dropped simultaneously from the top of a tower. The one that reaches the ground first is

Answer 1

Ignoring the air resistance, assuming uniform gravity , small velocity of throwing and flat ground , both hit the ground at the same time.

But say the velocity of throwing is very large.. of order km/sec..then you have to consider the curvature of earth. In this scenario the vertical distance of the horizontal ball is increased from the tower. So the ball which is dropped gently will hit ground first.

Again if the velocity is too high but little less than escape velocity(11.2 km/s approx ) then the horizontal ball will always fall but not hit the ground. It will orbit earth in an elliptical path.

At exactly the escape velocity it will escape from earth following a parabolic path.

Any further velocity and it will escape earth following a hyperbolic path

Answer 2

if we neglet air resistance ..

then both will reach at the same time