The left field wall at Fenway Park is 310 feet from home plate; the wall itself (affectionately named the Green Monster) is 37 feet high. A batted ball must clear the wall to be a home run. Suppose a ball leaves the bat 3 feet off the ground, at an angle of 45º. Use g 32 feet per second² as the acceleration due to gravity and ignore any air resistance. 

(a) Find parametric equations that model the position of the ball as a function of time. 

(b) What is the maximum height of the ball if it leaves the bat with a speed of 90 miles per hour? Give your answer in feet. 

(c) How far is the ball from home plate at its maximum height? Give your answer in feet. 

(d) If the ball is hit straight down the left field wall, will it clear the Green Monster? If it does, by how much does it clear the wall?