The height h(t) (in metres) of a stone thrown vertically upwards after t seconds is given by h(t)=−5t2+20t+3 for t≥0.
(a) Find the value(s) of t when the stone is at ground level (h=0).
(b) Determine the maximum height reached by the stone and the time at which it occurs.
(c) Draw a rough sketch of the graph of h against t, marking clearly the intercepts with the axes and the highest point. Explain the physical meaning of the zeros in this context.