The Rogers Centre in Toronto, Ontario, has a center field fence that is 10 feet high and

Chapter 12, Problem 31

(choose chapter or problem)

Projectile Motion In Exercises 25-38,use the model for projectile motion,assuming there is no air resistance.

The Rogers Centre in Toronto, Ontario, has a center field fence that is 10 1feet high and 400 feet from home plate. A ball is hit 3 feet above the ground and leaves the bat at a speed of 100 miles per hour.

(a) The ball leaves the bat at an angle of \(\theta=\theta_{0}\) with the horizontal. Write the vector-valued function for the path of the ball.

(b) Use a graphing utility to graph the vector-valued function for \(\theta_{0}=10^{\circ}, \theta_{0}=15^{\circ}, \theta_{0}=20^{\circ}, \text { and } \theta_{0}=25^{\circ}\). Use the graphs to approximate the minimum angle required for the hit to be a home run.

(c) Determine analytically the minimum angle required for the hit to be a home run.

Text Transcription:

theta=theta_0

theta_0=10 degrees, theta_0=15 degrees, theta_0=20, and theta_0=25 degrees