You are surely familiar with Newton's First Law of Motion. It says that if an object is at rest and no force is applied to it, that object will remain at rest; and that if an object is moving and no force is applied to it, that object will continue to move at constant speed in a straight line.
Perhaps you are also familiar with the fact that Newton's Second Law of Motion (the sum of the forces on an object = its mass times its acceleration) applies only if the motion is viewed from the point of view of an "Inertial Frame of Reference." This is a frame of reference that is itself either at rest or moving at constant speed in a constant direction. This means that (regardless of what the object is doing) the frame of reference in which it is being observed must be moving at constant velocity, and this means it must not be accelerated.
Understand this: You can observe an accelerating object in a non-accelerating frame of reference. For example, if you stand at a street corner you can observe a car that is speeding up (accelerating). So, even though the car is accelerating, the frame of reference from which you are observing that car is not accelerating, and is therefore an inertial frame of reference.
Put these ideas together, and you will conclude (correctly) that whereas a ball thrown horizontally normally appears to travel in a straight line if you observe it as usual from a non-accelerating frame of reference, it will not necessarily appear to travel in a straight line if its motion is observed from a non-inertial (accelerating) frame of reference. (In all of this discussion, we will ignore its vertical motion, which causes it to arc downward because of the pull of gravity).
In the next pages, we will find a way to show that a ball thrown horizontally, when viewed from an accelerating frame of reference may move in unexpected paths. The drawings above give you a hint of what you will discover.
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