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At the bottom of the swing the ball is at highest velocity. The ball will follow a parabolic path starting at the vertex and traveling horizontally, then falling off quickly until it hits the ground.
It would travel in a straight line until air resistance brought it to a standstill. It would then hover at that point - in mid-air forever. If air resistance is also removed from the scenario an even stranger thing will happen. The ball will continue in a straight line forever. But, because of the curvature of the earth, the earth's surface will drop away so that the ball will actually fly off into space. One problem with this thought experiment is that the concept of a "straight" line depends on gravity.
perpendicular to the ball's path
-- The only horizontal force on a thrown ball is the force of air resistance, so the horizontal acceleration is very small, and the horizontal speed stays almost constant. -- The vertical force on a thrown ball is the force of gravity, so the ball accelerates straight down at the acceleration of gravity. -- The result of unequal horizontal and vertical components of acceleration is a curved path.
If it is thrown at an angle, at the top of its path, its vertical velocity will be zero, however its horizontal velocity will be the same as its initial horizontal velocity minus whatever loss in speed as a result of air friction at that point. We won't know what that is without more information.
travel horizontally
The ball would continue straight without any gravitational forces acting on it, and without air resistance. If you consider air resistance, then the spin of the ball may give it a curved path, and eventually the ball would stop traveling as the air resistance slows down the ball.
The ball follows a parabolic path when thrown. In a vacuum (with no air or other forces acting upon it) the gravitational pull of the earth causes the ball to accelerate toward the earth (9.8m/sec
It will travel in a straight line as far as the x and z axises are concerned however in the Y axis the bodies path will be a inverted parabolic.
At the bottom of the swing the ball is at highest velocity. The ball will follow a parabolic path starting at the vertex and traveling horizontally, then falling off quickly until it hits the ground.
It doesn't matter whether the object is thrown down, up, horizontally, or diagonally. Once it leaves the thrower's hand, it is accelerated downward by an amount equal to acceleration of gravity on the planet where this is all happening. On Earth, if you throw an object horizontally, it accelerates downward at the rate of 9.8 meters per second2 ... just as it would if you simply dropped it. Whether it's dropped or thrown horizontally, it hits the ground at the same time.
Calculating the path of an object when acted on by a continual force (like a ball thrown where there is gravity)
It would travel in a straight line until air resistance brought it to a standstill. It would then hover at that point - in mid-air forever. If air resistance is also removed from the scenario an even stranger thing will happen. The ball will continue in a straight line forever. But, because of the curvature of the earth, the earth's surface will drop away so that the ball will actually fly off into space. One problem with this thought experiment is that the concept of a "straight" line depends on gravity.
Actually, if you were to ask a Gunners Mate in the Navy, he'd tell you that the curved path of an object thrown is called a trajectory. And in a practical case, trajectories are not parabolic when traveled in a gas, like our atmosphere. They are parabolic if and only if the objects are not also acted on by drag and angular momentum forces. And any good curve ball pitcher in baseball can prove that.
perpendicular to the ball's path
The rock follows a parabolic path.
-- The only horizontal force on a thrown ball is the force of air resistance, so the horizontal acceleration is very small, and the horizontal speed stays almost constant. -- The vertical force on a thrown ball is the force of gravity, so the ball accelerates straight down at the acceleration of gravity. -- The result of unequal horizontal and vertical components of acceleration is a curved path.