The position of a small plane coming into land at time t minutes after it has started its descent is modelled by the parametric equations x = 80t, y = −9.1t + 3000, 0 ≤ t ≤ 329 where x is the horizontal distance travelled (in metres) and y is the vertical distance travelled (in metres) from the point of starting its descent.

a. Find the initial height of the plane.

b. Justify the choice of domain, 0 ≤ t ≤ 329, for this model.

c. Find the horizontal distance the plane travels between beginning its descent and landing