Juggling Concept: Equal Accelerations, Opposite Velocities | Quick Question"

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In juggling, when two balls are thrown to the same height, their accelerations are equal while their velocities are equal and opposite at the halfway point. The acceleration due to gravity, denoted as g, is constant at all points in the motion. The sign of g depends on the chosen positive direction; if down is positive, g is positive, and if up is positive, g is negative. Regardless of the direction chosen, the upward velocity of one ball will always equal the downward velocity of the other. Understanding these principles is crucial for analyzing motion in juggling.
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A juggler throws two balls to the same height so that one is at the halfway point going up when the other is at the halfway point coming down. At that point:

Their accelerations are equal but their velocities are equal and opposite.

Right?
 
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Right.

Their accelerations are always g.

It doesn't matter what point you choose, whether half-way point, or no. The upward velocity will always be equal and opposite the downwards velocity.
 
but will the acceleration be -g at any point?
 
It alll depends upon which direction you call the positive direction.

g always acts downwards.

If you choose downwards as the +ve direction, then g will be taken as +ve, +g. And the acceleration will be +g at all points.

If you choose upwards as the +ve direction, then g will be taken as -ve, -g. And this time the acceleration will be -g at all points.
 
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