Physics

To solve this problem, we need to determine the fraction of the total mechanical energy that is kinetic energy at the highest point of the projectile's trajectory.

 

Understanding the Total Mechanical Energy

The total mechanical energy of a projectile is the sum of its kinetic energy () and potential energy ().

 

The total mechanical energy at any point in the projectile's motion is conserved and remains constant. Therefore, at launch, the total energy is:

where:

is the initial kinetic energy,

is the initial potential energy (where at ground level, so this term is initially zero).

 

At the highest point, the kinetic energy is related to the horizontal speed, while the vertical speed is zero. The potential energy at the highest point is maximum.

 

Kinetic and Potential Energy at the Highest Point

At the highest point:

- The vertical velocity is , so all the speed is horizontal.

- The horizontal velocity is .

- The kinetic energy at the highest point is:

 

The potential energy at the highest point is:

where

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