On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 216 feet. The path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the right of the pitcher’s mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?
To find the distance the outfielder throws the ball, we need to determine the distance from where the ball was caught to the pitcher's mound.
Let's denote the following:
- Distance from pitcher's mound to home plate = 60.5 feet
- Distance ball was hit = 216 feet
- Angle with the line connecting pitcher and catcher = 34°
Since the ball is hit at an angle, we need to find the vertical and horizontal components of the ball's path.
Vertical component = 216 * sin(34°) = 216 * 0.559 = 120.744 feet
Horizontal component = 216 * cos(34°) = 216 * 0.829 = 178.764 feet
Now, we know that the distance from where the ball was hit to the pitcher's mound is the same as the horizontal component of the ball's path. So, the distance from where the ball was caught to the pitcher's mound is also 178.764 feet.
Therefore, the outfielder throws the ball a distance of 178.764 feet to get it back to the pitcher on the mound.