Answer:
When the ball hits the ground, its height will be 0 meters. Therefore, we need to solve the equation:
h(t) = 0
8t - 5t^2 + 4 = 0
We can solve this quadratic equation by factoring or by using the quadratic formula, but in this case, it's easier to use factoring:
(5t - 4)(t - 1) = 0
From this equation, we can see that either 5t - 4 = 0 or t - 1 = 0. Solving for t in each case, we get:
5t - 4 = 0 ==> t = 0.8 seconds
t - 1 = 0 ==> t = 1 second
Therefore, the ball will reach the ground after either 0.8 seconds or 1 second, depending on the initial height of the ball.