A47.0-g golf ball is driven from the tee with an initial speed of 52.0 m/s and rises to a height of 24.6 m. (a) neglect air resistance and determine the kinetic energy of the ball at its highest point.

The initial kinetic energy is the total energy of the ball for its whole flight. As it rises some of it becomes potential energy as its vertical motion stops and changes direction. So the initial energy is (1/2)(0.047)(52)^2=63.544J. When at its peak its potential energy is E=mgh, or E=(0.047)(9.81)(24.6)=11.34. This is now "missing" from the kinetic energy it started with so now KE=63.544-11.34=52.2J

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