Why Is Initial Velocity Equal to Final Velocity in Parabolic Motion?

AI Thread Summary
In parabolic motion, when an object is launched and lands at the same height, its initial and final velocities are equal due to the symmetry of the trajectory. The object experiences constant gravitational acceleration of approximately 9.8 m/s² throughout its flight, affecting both the upward and downward motion equally. This symmetry means that the speed at which it is launched will match the speed at which it impacts the ground. The angle of launch also plays a role in determining the trajectory but does not affect the equality of initial and final velocities. Thus, the principles of physics governing projectile motion confirm that initial velocity equals final velocity in this scenario.
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Homework Statement


I was wondering, when an object's motion is in the shape of a parabola, and it lands at the same height that it was shot from.. why would the initial velocity and the angle from the ground at which it was shot from.. be equal to the final velocity at which it hit the ground?


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Would it be because of its parabolic shape?
 
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Because both when moving upwards and downwards the same gravitational force is working on the object. It's acceleration is always ~9.8 m/s^{2} and directed to Earth's center.
 

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