Question

modeling real life in a volleyball game, a player on one team spikes the ball over the net when the ball is 10 feet above the court. the spike drives the ball downward with an initial vertical velocity of 55 feet per second. write a function that represents the situation. use h for height (in feet) and t for time (in seconds).

Explanation:

Step1: Recall the vertical motion model

The vertical motion model is \(h = - 16t^{2}+v_{0}t + h_{0}\), where \(v_{0}\) is the initial velocity and \(h_{0}\) is the initial height.

Step2: Identify the values of \(v_{0}\) and \(h_{0}\)

Given that the initial vertical velocity \(v_{0}=55\) feet per - second and the initial height \(h_{0} = 10\) feet.

Step3: Substitute the values into the formula

Substitute \(v_{0}=55\) and \(h_{0}=10\) into the formula \(h=-16t^{2}+v_{0}t + h_{0}\). We get \(h=-16t^{2}+55t + 10\).

Answer:

\(h=-16t^{2}+55t + 10\)