In Exercises consider a projectile launched at a height h feet above the ground and at an angle with the horizontal. When the initial

In Exercises 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 vo feet per second, the path of the projectile is modeled by the parametric equations x = (v₀ cos θ)t and y = h + (v₀ sin θ)t - 16t².

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 (see figure).

(a) Write a set of parametric equations for the path of the ball.

(b) Use a graphing utility to graph the path of the ball when θ  = 15°. Is the hit a home run? 

(c) Use a graphing utility to graph the path of the ball when θ = 23°. Is the hit a home run?

(d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run.

3 ft 400 ft $10 ft