Objective: Using your knowledge of calculus, find a cubic polynomial f(x) = ax3 + bx2 + cx + d to model the approach path for a landing aircraft. The function f(x) will be the height of the plane from the ground, and x the ground distance of the plane away from the airport. Both distances are measured in miles and the function is subject to the following conditions:

The plane is cruising at an altitude of 35,000ft and begins its descent from a perfectly horizontal

position 65mi from the airport.

The arrival airport is located at the origin.

Find the coefficients of the cubic polynomial a, b, c, and d to plug into the airplane's computer. Enter

numbers only, rounded to 5 decimal places. As a reminder, so as to not introduce rounding errors, never round during intermediate steps Check your answer using a graphing calculator to make sure the graph of f(x) with your coefficients, for x between 0 and 65mi, looks like the path of a descending plane. Include the graph of your function, for x between 0 and 65mi, in your final submission. Next, we want to investigate whether the acceleration induced by the aircraft's trajectory is safe and tolerable for the aircraft's passengers. Assume that the horizontal velocity at the beginning of the descent (at the horizontal distance of 65mi) is -450 miles per hour and that the horizontal distance decreases linearly with time. (Discuss here also as to which extent this is a reasonable assumption or not).

Research on which accelerations are still tolerable for the human body. Based on the mentioned

the assumption, calculate the maximal vertical acceleration that is induced on the passengers throughout the aircraft's approach to landing and discuss whether this poses a potential threat to the health of the passengers.