Final answer:
The maximum height reached by the rocket is found using the vertex formula of the given quadratic function. By calculating the time at which the vertex occurs and substituting it back into the function, we find that the maximum height is 224 feet, which is not listed in the provided options.
Step-by-step explanation:
To find the maximum height the rocket reaches, we can use the vertex formula of a parabola. The given function for the height of the rocket as a function of time is f(t) = -16t^2 + 64t + 160. Since the coefficient of t^2 is negative, the parabola opens downward, and the vertex represents the maximum height.
The time at which the rocket reaches the maximum height is given by t = -b/2a from the vertex formula, where a is the coefficient of t^2 and b is the coefficient of t. Substituting the values, we get t = -64/(2*(-16)) = 2 seconds.
Plugging this time back into the function to find the height at t = 2, we get f(2) = -16(2)^2 + 64(2) + 160. Simplifying this expression, we find the maximum height to be f(2) = -64 + 128 + 160 which equals 224 feet. Therefore, the correct answer is not among the given options (A. 80 ft, B. 90 ft, C. 70 ft, D. 100 ft).