Answer:
<h2>a. 41.5 ft</h2><h2>b. 41.5 ft.</h2><h2>c. 90°.</h2>Step-by-step explanation:
Notice that a baseball diamond is a square, which means all sides are equal. In this case, each side is 65 feet long.
It's important that a square is a symmetric figure, as a symmetric quadrilateral, its diagonals are congruent and the bisect each other. That means that the distance from every corner to the center is the same.
a. Based on square definitions, the distance from the pitching rubber to first base is 41.5 feet.
b. Based on square definitions, the distance from the pitching rubber to second base is 41.5 feet.
c. if the pitcher faces the home plate, he needs to turn his 90° to face the first base, that is because diagonals are perpendicular each other, which means they have a right angle between.
The position function of a particle is given by:
The velocity function is the derivative of the position:
The particle will be at rest when the velocity is 0, thus we solve the equation:
The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
Substituting:
We have two possible answers:
We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6: