The height h (in metres) of a small ball thrown straight upward is modelled by the polynomial function
h(t)=−5t2+20t+1.5,
where t is the time in seconds after the ball is released.
(i) Determine the y-intercept of the graph of h.
(ii) Interpret the result obtained in part (i) in the context of the physical situation.
(iii) If the ball is caught at the same height from which it was thrown, find the total time the ball remains in the air. (Hint: One of the intercepts has already been found in part (i).)