Find the solution of the given linear equation.
A parachutist exits a plane at 1067 M. She counts a specified number of seconds before opening her chute. The equation describing her height above the ground during the free fall is h = -4.9t2 + 1067, where the height h is measured in meters and time t in seconds. After she opens her chute, the equation describing her height above the ground is h = -4.4t + 890.
At the point at which she opens her parachute, height h and time t are the same for both equations.
i) Solve the linear-quadratic system algebraically
h = -4.9t2 +1067
h = -4.4t + 890
To determine the time and the height at which she opens her parachute.
ii) Illustrate your result graphically, showing the two functions and the point(s) of intersection.
iii) If a line and a parabola are drawn on the same grid, do they always intersect at one point? What other possibilities are there? Explain your answer using diagrams as necessary.