We can solve the problem by using the law of conservation of energy.
At the starting point, the ball has only kinetic energy, since its height is zero, so:
[tex]E_i = K_i = \frac{1}{2}mv_i^2= \frac{1}{2} (0.047 kg)(54.0 m/s)^2 = 68.5 J [/tex]
At its highest point, the ball has both potential energy and kinetic energy:
[tex]E_f = U_f + K_f [/tex]
we can find the potential energy of the ball at its highest point:
[tex]U_f = mgh=(0.047 kg)(9.81 m/s^2)(24.6 m)=11.3 J[/tex]
For the law of conservation of energy, the initial mechanical energy should be equal to the final mechanical energy:
[tex]E_i = E_f[/tex]
which becomes
[tex]K_i = U_f + K_f[/tex]
that we can solve to find the kinetic energy of the ball at its highest point:
[tex]K_f = K_i-U_f = 68.5 J- 11.3 J=57.2 J[/tex]
