Question

A volleyball is hit into the air during a serve. The height of the volleyball can be modeled by the equation y = -16t² + 28t + 7, where y is the height of the volleyball in feet t seconds after the ball is hit. How long is the volleyball in the air? Please answer with a sentence that puts your answer in context.

Answer 1

The volleyball is in the air for approximately 3.79 seconds.

Step-by-step explanation:

To find the length of time the volleyball is in the air, we need to find the values of t when the height of the volleyball is 0. This is because when the ball is on the ground or has hit the ground, its height is 0.

We can set y = 0 in the equation y = -16t² + 28t + 7 and solve for t. This gives us a quadratic equation: -16t² + 28t + 7 = 0.

Using the quadratic formula, we can find the values of t to be t = 3.79 seconds and t = 0.54 seconds. Since the ball is on the ground at t = 0, we can ignore this solution. Therefore, the volleyball is in the air for approximately 3.79 seconds.