A shortstop is standing in the base path between second and third base when she fields the ball. She is 30 feet from second base and needs to make the throw to first base. Assuming the field is square and the side length is 90ft, she needs to throw the ball approximately?

Answer 1

To determine how far the shortstop needs to throw the ball to first base, we can use the coordinates of the bases to guide us.

Assuming the baseball diamond is a square:

• Second base (SB) is at the coordinates (90, 90).
• First base (FB) is at (0, 90).
• The shortstop is 30 feet away from second base, which puts her at (90, 60) on a coordinate grid.

Now, to find the distance from the shortstop's position (90, 60) to first base (0, 90), we can use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting in the coordinates:

• \(x_1 = 90, y_1 = 60\) (shortstop’s position)
• \(x_2 = 0, y_2 = 90\) (first base)

So, we get:

\[ d = \sqrt{(0 - 90)^2 + (90 - 60)^2} \] \[ d = \sqrt{(-90)^2 + (30)^2} \] \[ d = \sqrt{8100 + 900} \] \[ d = \sqrt{9000} \] \[ d \approx 94.87 \text{ feet} \]

Thus, the shortstop needs to throw the ball approximately 94.87 feet to reach first base.

Answer 2

Lets round to 94.9, k?