Ball \(A\) is released from rest at a height \(b\) above the ground. Ball \(B\) is launched upward from the same height at initial speed \(v_{\mathrm{B}, \mathrm{i}}\). The two balls have the same inertia \(m\). Consider this motion from the instant they are released to the instant they hit the ground.

(a) Using kinematics, show that the change in kinetic energy is the same for both balls.

(b) Show that this change in kinetic energy is equal to the negative of the change in the gravitational potential energy of the Earth-ball system between positions \(x=+h\) and \(x=0\).