When comparing the heights reached by two identical cannonballs shot straight up with different initial velocities, the conservation of energy principle applies, where total energy equals kinetic plus potential energy. The first cannonball, having 2.0 times the initial velocity of the second, will reach a height proportional to the square of its velocity, leading to a height increase of four times compared to the second cannonball. As the cannonballs ascend, their kinetic energy converts to potential energy until they momentarily stop at their peak height. To solve for the final position, kinematic equations involving initial and final velocity, acceleration due to gravity, and displacement should be utilized. Understanding these concepts and equations is crucial for accurately determining the heights achieved by each cannonball.
