To solve for the initial velocity of a ball thrown upwards from a 30m cliff that hits the ground in 3.0 seconds, kinematic equations for uniformly accelerated motion can be applied. The relevant equation is s = ut + 0.5at², where s is the displacement, u is the initial velocity, a is the acceleration (which is -9.81 m/s² due to gravity), and t is the time. By substituting the known values into the equation, the initial velocity can be calculated. The problem emphasizes understanding the relationship between time, displacement, and initial velocity in uniformly accelerated motion. Ultimately, applying these concepts leads to determining the ball's initial velocity.