Who Will Get the Out?

The Atlanta Braves are playing the New York Yankees. It should be a great game, and the fans are excited. Hometown hero and right fielder for the Braves, Nick Markakis, and the Braves’ center fielder, Ender Inciarte, are sure to be challenged by some great Yankee hitters. They will be racing each other as balls are hit their way. Let’s play ball!

Aaron Judge is at bat for the Yankees. He is known for being their ace hitter. Pitcher Mike Foltynewicz is on the mound for the Braves. Judge gets called strikes on the first two pitches, but swings hard at the third pitch. He hits a line drive between first and second base. Both Markakis and Inciarte race for the ball. Who will get there first? Will they get there in time to make the out?

  1. The batter is hitting from the point (0,0). The ball follows a path of the equation y = x. Draw and label this line(with the letter b) on your baseball coordinate plane.
  1. Inciarte is at a starting point of (150,200). He races towards the ball at a path of the equation y = 200. LabelInciarte’s starting point and draw his running path, labeled with the letter “I” on your baseball coordinate plane.
  1. Markakis is at a starting point of (200, 50). He races towards the ball at a path of the equation y = 3x – 550. Label his starting point and draw his running path, labeled with the letter “m” on your baseball coordinate plane.
  1. Assuming they are running at the same speed, who do you think will reach the ball first?
  1. Why do you think this?
  1. What are the coordinates for where the ball intersects the path of the first outfielder to reach it? (use your knowledge of systems of equations to calculate this.)
  1. What is the distance from Inciarte’s starting point to the point where he intersects the path of the ball?
  1. If Inciarte can run at a speed of 28, how long does it take him to reach the ball?
  1. What is the distance from Markakis’ starting point to the point where he intersects the path of the ball?(use the Pythagorean theorem or the distance formula)
  1. If Markakis can run at a speed of 26 , how long does it take him to reach the ball?
  1. What is the distance the ball travels from home plate at (0,0) to the point of intersection with Inciarte?(use the Pythagorean theorem or the distance formula)
  1. If the ball is traveling at a speed of 75 , (110 ), how long will it take it to reach Inciarte’s point of intersection with it?
  1. Will either player reach the ball in time to catch it? Why or why not?

Now it is time for Yankees batter Brett Gardner to face Foltynewicz. The first two pitches are balls, the third is a called strike, but Gardner swings at the fourth pitch and also hits a line drive.

  1. The batter is hitting from the point (0,0). The ball follows a path of the equation y = x. Draw and label (with the letter b) this line on your baseball coordinate plane.
  1. Inciarte is at a starting point of (150,200). He races towards the ball at a path of the equation x = 150. Label Inciarte’s starting point and draw his running path, labeled with the letter “I”, on your baseball coordinate plane.
  1. Markakis is at a starting point of (200, 50). He races towards the ball at a path of the equation y = -x + 250. Label his starting point and draw his running path, labeled with the letter “m” on your baseball coordinate plane.
  1. Assuming they are running at the same speed, who do you think will reach the ball first?
  1. Why do you think this?
  1. What are the coordinates for where the ball intersects the path of the first outfielder to reach it? (use your knowledge of systems of equations to calculate this.)
  1. What is the distance from Inciarte’s starting point to the point where he intersects the path of the ball?
  1. If Inciarte can run at a speed of 28, how long does it take him to reach the ball?
  1. What is the distance from Markakis’ starting point to the point where he intersects the path of the ball?
  1. If Markakis can run at a speed of 26 , how long does it take him to reach the ball?
  1. What is the distance the ball travels from home plate at (0,0) to the point of intersection with Inciarte?
  1. If the ball is traveling at a speed of 75 , (110 ), how long will it take it to reach Inciarte’s point of intersection with it?
  1. Will either player reach the ball in time to catch it? Why or why not?