A physics club designs an experiment on a seaside cliff to study two-dimensional motion. A launcher placed at the cliff edge fires identical steel spheres with the same initial speed but at different angles. Each sphere lands either on a sandy ledge partway down the cliff or on the beach below.
The cliff edge is taken as vertical position y=0. Sphere A is launched at 35∘ above the horizontal and lands on a ledge at y=+4m. Sphere B is launched at 20∘ above the horizontal and lands on the beach at y=−18m. Neglect air resistance and let the magnitude of the gravitational field be g=9.8m/s2.
(a) Describe qualitatively how the vertical displacement of each sphere determines the form of the algebraic equation that must be solved to obtain its flight time.
(b) For Sphere A, explain why the time equation can admit two positive roots and state the physical meaning of each root.
(c) For Sphere B, argue whether one or two positive time roots are possible and justify your conclusion in terms of the launch and landing heights.
(d) Without performing detailed calculations, compare the total flight times of Sphere A and Sphere B. Support your answer with clear physical reasoning.