Question

A volleyball is hit into the air during a serve. The height of the volleyball can be modeled by the equation y = -16t^2 + 28t + 7, where y is the height of the volleyball in feet t seconds after the ball is hit. What is the maximum height of the volleyball?

A) The maximum height of the volleyball is 49 feet.
B) The maximum height of the volleyball is 28 feet.
C) The maximum height of the volleyball is 7 feet.
D) The maximum height of the volleyball is 16 feet.

Answer 1

The maximum height of the volleyball is 49 feet.

Step-by-step explanation:

The maximum height of the volleyball can be found by identifying the highest point in the trajectory, which is when the vertical velocity is zero. In this case, the equation y = -16t^2 + 28t + 7 represents the height of the volleyball. To find the maximum height, we need to find the time when the vertical velocity is zero. This can be done by setting the derivative of the equation equal to zero:

dy/dt = -32t + 28 = 0

Solving for t, we get t = 7/8 seconds. Substituting this value back into the equation, we can find the maximum height:

y = -16(7/8)^2 + 28(7/8) + 7 = 49 feet.

Therefore, the maximum height of the volleyball is 49 feet.