Question

A ball is hit into air at time t=0 seconds.its height above the ground is given by the equation h=25t-9.8t².what is the value of t when the ball lands on the ground?

Answer 1

The ball lands on the ground at t=2.55 seconds

Explanation:

Quadratic Equation

The following function models the height above the ground of a ball hit into the air at time t seconds:

`h=25t-9.8t^2`

We need to find the value of t when the ball hits the ground.

At ground level, h is zero, thus:

`25t-9.8t^2=0`

This is an incomplete quadratic equation that can be easily solved by factoring:

`t(25-9.8t)=0`

There are two solutions:

t=0

t=25/9.8=2.55 s

The first solution corresponds to the moment when the ball is hit, and the second is when it returns to the ground, thus:

The ball lands on the ground at t=2.55 seconds