Does velocity affect the kinetic energy of falling objects?

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SUMMARY

The discussion clarifies that the kinetic energy (KE) of three identical balls thrown from a cliff—one upward, one downward, and one horizontally—is equal just before impact. Despite initial perceptions, the upward-thrown ball (Ball 1) returns to the cliff's edge with the same speed it was thrown, thus equating its kinetic energy to that of the other two balls. The formula KE=1/2MV^2 confirms that all three balls possess the same kinetic energy upon reaching the ground, as their velocities are identical at that moment.

PREREQUISITES
  • Understanding of basic physics concepts, particularly kinetic energy.
  • Familiarity with the equation KE=1/2MV^2.
  • Knowledge of projectile motion and its effects on velocity.
  • Basic grasp of gravitational acceleration and its impact on falling objects.
NEXT STEPS
  • Study the principles of projectile motion in physics.
  • Explore the concept of energy conservation in falling objects.
  • Learn about the effects of air resistance on falling bodies.
  • Investigate the relationship between velocity and kinetic energy in different contexts.
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Students of physics, educators teaching mechanics, and anyone interested in understanding the principles of motion and energy in falling objects.

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Three identical balls are thrown from the edge of a cliff, each with the same initial speed. Ball 1 is thrown directly upward. Ball 2 is thrown directly downward. Ball 3 is thrown horizontally. Which of the following statements correctly characterizes the relative kinetic energies (K) of the three balls just before hitting the ground.

The correct answer for this is that theyre all equal, but that doesn't make sense to me. If the first ball is thrown directly upward, then when its done climbing the top, it will have more time to accelerate downward than all the other balls. The more time it has to accelerate, the faster it's velocity will become, and KE=1/2MV^2, so the larger the velocity, the larger the KE. And ball 2 and 3 having the same KE makes sense, but I figured ball 1 should be greater. Where did I go wrong?
 
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Determine the velocity when the first ball, falling down from the top height, reaches the edge of the cliff again. You will see that it is equal in magnitude as the initial velocity was. From here, it moves as ball 2. ehild
 

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