A student drops her phone from her apartment balcony on the fourth floor, which is 36 feet from the ground. For this problem, use that a falling object has the position function s( t )= 1/2^2+v0t+s0 , where s(t) represents the height in feet as a function of time t represents time in seconds LaTeX: v_0v 0 represents the initial velocity LaTeX: s_0s 0 represents the initial height the object starts at a represents the acceleration of a falling object. Unless told otherwise, use LaTeX: a=g=-32\frac{ft}{\sec^2}a = g = − 32 f t sec 2, which means we are ignoring air resistance and simply using the effect of gravity.
Use the above information to answer the following questions:

a. What is the position function? Be sure to give your answer in proper function notation.
b. What is the velocity function? Be sure to give your answer in proper function notation.
c. What is the acceleration function? Be sure to give your answer in proper function notation.
d. When will the phone hit the ground? How did you find this?
e. With what velocity will the phone hit the ground? How did you find this?
f. How fast is the phone accelerating when it is falling? How do you know this?