The path of a ski jumper from the point of leaving the ramp to the point of landing is modelled using the parametric equations x = 18t, y = −4.9t² + 4t + 10, 0 < t < k where x is the horizontal distance in metres from the point of leaving the ramp and y is the height in metres above ground level of the ski jumper, after t seconds.

a. Find the initial height of the ski jumper.

b. Find the value of k and hence state the time taken for the ski jumper to complete her jump.

c Find the horizontal distance the ski jumper jumps.

d. Show that the ski jumper’s path is a parabola and find the maximum height above ground level of the ski jumper.