This is the boss. No calculator — today $g = 10\ \mathrm{m/s^2}$, stated on the paper, and every draw is chosen to fit in your head. One ball, one long problem, and every answer feeds the next: the apex time (that is the VERTEX of $h(t) = v_0 t - 5t^2$), then the height it buys, then the hang time (that is a ROOT), and finally Vieta signs the audit. Write each line down — one early slip rides the parabola all the way back to the ground.

Every tool from the chapter plays: vertex, roots, and the sum-of-roots check closing the loop. 5★ under par here is the chapter crown. Serve.