Consider a projectile launched at a height h feet above the ground and at an angle θ with the horizontal. When the initial velocity is v₀ feet per second, the path of the projectile is modeled by the parametric equations:
The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 3 feet above the ground. It leaves the bat at an angle of θ degrees with the horizontal at a speed of 100 miles per hour.
(a) Write a set of parametric equations for the path of the ball.
(b) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run.