Question

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, she needs to throw the ball approximately what?

Answer 1

To determine the distance the shortstop needs to throw the ball to first base, we can visualize the baseball field as a square diamond. The bases are positioned at the four corners of the square:

- Home plate (A)
- First base (B)
- Second base (C)
- Third base (D)

The distance between each pair of consecutive bases (e.g., from home plate to first base, first base to second base, etc.) is typically 90 feet in a standard baseball field.

From the information provided:
- The shortstop is 30 feet from second base (C).
- The first base (B) is located at coordinates (90, 0) if we assume home plate (A) is at the origin (0, 0), second base (C) at (90, 90), and third base (D) at (0, 90).

To find the shortstop's position, we can place her between second base and third base, specifically 30 feet from second base. Since she is 30 feet towards third base, her coordinates will be approximately (90, 90 - 30) or (90, 60).

Now, we need to calculate the distance from her position to first base. The coordinates for first base (B) are (90, 0).

We can find the distance between the shortstop's location (90, 60) and first base (90, 0) using the distance formula:

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

Here, \((x_1, y_1) = (90, 60)\) and \((x_2, y_2) = (90, 0)\):

\[
d = \sqrt{(90 - 90)^2 + (0 - 60)^2}
\]
\[
d = \sqrt{0 + (-60)^2}
\]
\[
d = \sqrt{3600}
\]
\[
d = 60 \text{ feet}
\]

Thus, the shortstop needs to throw the ball approximately **60 feet** to reach first base.