4. An arrow is shot upward from the top of a hill. Its height (in metres) above a reference point on the hill after t seconds is modelled by the polynomial
s(t)=−4t2+kt+9,
where k is a positive constant depending on the speed of projection.
(a) Using the condition that the arrow must eventually return to the reference level, obtain the inequality that k must satisfy so that s(t) has real zero(s).
(b) If k=2, determine whether the arrow will return to the reference level. Give reason.
(c) For k=10, find the time taken for the arrow to return to the reference level and state which root corresponds to this event.