Question

Pedro throws a ball upward at a rate of 20 meters per

second from an initial height of 2 meters. The height
of the ball above the ground can be approximated by
h = -512 + 20t + 2, where t represents the amount of time,
in seconds, since the ball has been released.
What is the maximum height that the ball reaches?

Answer 1

The maximum height that the ball reaches is -530 meters.

Step-by-step explanation:

To find the maximum height that the ball reaches, we need to find the vertex of the quadratic equation that represents its height.

The equation given is h = -512 + 20t + 2.

The vertex of a quadratic equation in the form h = at^2 + bt + c is given by t = -b/2a.

Plugging in the values from the equation, we have t = -20/(2*10) = -1.

The maximum height occurs at t = -1, which can be substituted back into the equation to find the height:

h = -512 + 20*(-1) + 2 = -512 -20 + 2 = -530 meters.

Therefore, the maximum height that the ball reaches is -530 meters.