Derive the formulas for time of flight, range, and maximum height in the case that an object is launched from the initial position (0.yn) with initial velocity vol (cosa, sin ). Recall that the acceleration function is defined as a(t) = (0, -g). Integrate this function to find the velocity function. v(t) = Use the initial velocity to determine the arbitrary constant C, then combine the vectors. v(t) = Next, integrate the velocity function to find the position function. r(t) = OA. T= Use the initial position to determine the arbitrary constant C, then combine the vectors. r(t) = Finally, use the fact that when the vertical component of the position function is equal to zero, the object has landed, to find the time of flight. Choose the correct answer below. O B. T= OC. T= OD. T= Vo sina+ Vo cos a + 1 g -C Vo sina+2gyo g 2 Vosin +4gyo 2g 2 2gyo+vo sin 2% +2|vo| cos a g +C