Final answer:
The equation that could represent the height of the stuntman as a function of time, given no initial velocity and ignoring air resistance, is h(t) = 39 - 16t², where h is the height in feet and t is the time in seconds.
Step-by-step explanation:
The height of the stuntman as a function of time can be represented by the equation of free-fall motion under the influence of gravity, given that there is no initial velocity. The standard equation for this scenario is h = h0 - ½gt², where h0 is the initial height (39 feet), g is the acceleration due to gravity (approximately 32 feet per second squared in the Imperial system or 9.8 meters per second squared in the SI system), and t is time in seconds. Since we are discussing the fall in feet, we will use the Imperial system for this problem. Converting feet to meters is not necessary because the equation must be consistent with the units given in the problem statement.
If you want to start your time accounting from the moment the stuntman starts to fall, the equation simplifies to h(t) = 39 - 16t². In this scenario, 't' is the time in seconds from the moment of the stuntman beginning the fall, and 'h(t)' would represent the height above the ground at time 't'.