You hit a tennis ball with an initial vertical velocity of 25 m/s. The ball leaves the tennis racket 2 meters above the ground, h_o. How much time does your opponent have before the ball hits the ground on the other side of the net, h(t)? Use h(t) = -5t^2 + v_0t + h_0 where h(t) is the height of a tennis ball being hit h_0 is the initial height v_0 is the velocity in meters/second after time (t) in seconds

Solving a quadratic equation, it is found that your opponent has 5.08 seconds to react before the ball hits the ground on the other side of the net.

What is the quadratic equation for the ball's height?

It is given by:

[tex]h(t) = -5t^2 + v_0t + h_0[/tex]

In which:

[tex]v_0[/tex] is the initial velocity of the ball.

[tex]h_0[/tex] is the initial height of the ball.

You hit a tennis ball with an initial vertical velocity of 25 m/s. The ball leaves the tennis racket 2 meters above the ground, hence [tex]v_0 = 25, h_0 = 2[/tex].

Then, the equation is:

[tex]h(t) = -5t^2 + 25t + 2[/tex]

It hits the ground when h(t) = 0, hence:

[tex]-5t^2 + 25t + 2 = 0[/tex]

The solutions are h = 5.08 and h = -0.08.

Since time is a positive measure, your opponent has 5.08 seconds to react before the ball hits the ground on the other side of the net.

More can be learned about quadratic equations at https://brainly.com/question/24737967