Understanding the trajectory of a projectile?

Question

It is stated that a projectile's motion can be divided into individual vectors. Now according to the laws of physics, the forces acting in the y-direction will never cancel or affect the force acting in the x-direction. Hence the weight $mg$ and the horizontal force $F$ are independent of one another. If that is the case, then why does a ball take longer to reach the ground if the horizontal force acting on it is large? Imagine it this way, a ball machine shoots a ball with a great force in the x direction, then why is it that the ball takes longer to fall when the x component is so large? Shouldn't the force $mg$ cause a constant downward acceleration? I understand that in case the x component is very large, the distance covered will naturally be greater but I'm speaking in terms of time taken for it to reach the ground.

Answer 1

By the way, by definition, a projectile is an object under the influence of only gravitational acceleration. Thus, the only force on it is the force of gravity, which is only vertical. So no horizontal force should be acting on it while it is a projectile. If it is launched, for example, it does not become a projectile until AFTER the launching force has done its job and been removed, and the object is flying through the air (with no air resistance).

Answer 2

The short answer: In your example, the ball does NOT take longer to reach the ground!!

If you throw--or otherwise propel-- an object, and there is no air friction, the time to reach the ground is a function of only three things:

--the mass of the object

--the initial vertical velocity

--the initial height

The horizontal velocity has no effect.