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If a velocity vector of an object can be divided into an x and y component relative to a second object's position, and both objects have gravity that attracts both objects to each other. We then know that the object is not moving in a straight path. How is the object able to move in 2 directions at once(x and y component of velocity). If you infinitely slowed down time to observe the movement of the object, would you see short frames where the object is only moving only vertically, then moving only horizontally, and alternating between both? Can someone explain the physics behind why what I'm saying is inaccurate.

p.s I just started learning physics (gr 11), so I might not understand extremely complex explanations.

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    $\begingroup$ The real world doesn't have $(x,y)$ coordinates. They're just there as a way of labelling the direction something is moving, but that something doesn't have to be moving on a literal grid. $\endgroup$ – jacob1729 May 15 '19 at 16:33
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    $\begingroup$ Rotate your X and Y axes such that the motion seems to be along either of them, and you'll interpret it as moving along only one direction $\endgroup$ – Eagle May 15 '19 at 17:05
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You need to understand that the "components" of velocity are all mathematical constructs, mainly linear algebra. They do not have a physical manifestation. It is a tool for us to be able to study a physical system using equations. Nature does not work that way.

So in reality, the object is moving in a single direction. If you slowed it down enough, it would appear to move in the very same direction.

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An object that follows a trajectory moves instantaneously in one only direction, the one tangent to the trajectory in that point. This is true regardless of the trajectory as long as you are able to draw it (fractal trajectories are a bit more complex).

The presence of two components in the velocity in your problem depends on how many dimensions the subspace containing the whole trajectory has. In your problem the whole motion will always lay in a fixed 2D plane (even if the space in which you observe the system has 3D).

Therefore you will write the unique direction of the trajectory as a combination of two directions that you arbitrarily pick as coordinates in the 2D plane: summing the x and y component of the velocity you obtain a vector which points in one direction (fixed by the ratio of the x and y components); that is the direction of the trajectory.

If the trajectory was 3D you would use three different components to keep track of its direction at a given point: the x, y and z components of the velocity for instance. If you were in a N dimensional space you could have up to N-dimensional trajectories, whose direction (a vector in a N dimensional space) can be written as a sum of N different components, your coordinates. But is all the same one vector, i.e. one direction.

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