Question

A 2nd baseman throws a baseball toward the 1st baseman 60 feet away. The path of the ball is given by f(x)=-0.004x^2+0.3x+6, where f(x) is the height of the ball (in feet) and x is the horizontal distance from the 2nd baseman (in feet). The 1st baseman can reach 8 ft high. Can the 1st baseman catch the ball without jumping?

Answer 1

The 1st baseman can't catch the ball without jumping.

Explanation:

To know if the 1st baseman can catch the ball without jumping we need to find the height reached by the baseball by solving the following equation:

`f(x) = -0.004x^(2) + 0.3x + 6`

We know that x (the horizontal distance) = 60 feet, so we have:

`f(60) = -0.004(60)^(2) + 0.3(60) + 6`

`f(60) = 9.6 ft`

Since the 1st baseman can reach 8 ft high and the height reached by the baseball is 9.6 ft, the 1st baseman can't catch the ball without jumping.

Therefore, the 1st baseman can't catch the ball without jumping.

I hope it helps you!