Question

a ball is thrown straight upward. a position function ( s(t)=\frac{1}{2} g t^{2}+v_{0} t+s_{0} ) can be used to describe the balls height, ( s(t) ), in feet, after ( t ) seconds. a graph of the balls height is shown to the right. complete parts a through c below. b. find and interpret ( s(3.25) ). ( s(3.25)=0 ) (simplify your answer.) interpret ( s(3.25) ). choose the correct answer below. a. the ball hits the ground 3.25 seconds after it is thrown. b. the ball is below ground 3.25 seconds after it is thrown. c. the ball is half its highest height 3.25 seconds after it is thrown. d. the ball hits its highest height 3.25 seconds after it is thrown. c. after how many seconds does the ball reach its maximum height? what is its maximum height? the ball reaches its maximum height after 2 seconds. (type an integer or a decimal.)

Explanation:

Step1: Analyze the position function meaning

The position function \(s(t)\) gives the height of the ball at time \(t\). When \(s(t)=0\), it means the height of the ball is \(0\) (ground - level).

Step2: Interpret \(s(3.25) = 0\)

Since \(s(t)\) represents the height of the ball at time \(t\), when \(t = 3.25\) and \(s(3.25)=0\), it implies that the height of the ball is \(0\) at \(t = 3.25\) seconds.

Answer:

A. The ball hits the ground 3.25 seconds after it is thrown.