The function $h(t)=-3 t^{2}+5 t+22$ describes the height of a ball, where $h$ is the ball's height in meters and $t$ is the time in seconds after the ball is hit. How long will it take until the ball lands? Round your answer to the nearest tenth.
It will take seconds for the ball to land on the ground.

Step 1 ：The function \(h(t)=-3 t^{2}+5 t+22\) describes the height of a ball, where \(h\) is the ball's height in meters and \(t\) is the time in seconds after the ball is hit. We need to find out how long it will take until the ball lands.

Step 2 ：The ball lands when its height is zero, i.e., when \(h(t) = 0\). So, we need to solve the equation \(-3t^2 + 5t + 22 = 0\) for \(t\).

Step 3 ：This is a quadratic equation, and we can solve it using the quadratic formula \(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = -3\), \(b = 5\), and \(c = 22\).

Step 4 ：Substituting the values of \(a\), \(b\), and \(c\) into the quadratic formula, we get two solutions, but we are interested in the positive one because time cannot be negative.

Step 5 ：The solutions are \(t1 = -2.0\) and \(t2 = 3.6666666666666665\). Rounding \(t2\) to the nearest tenth, we get \(t = 3.7\) seconds.

Step 6 ：Final Answer: It will take approximately \(\boxed{3.7}\) seconds for the ball to land on the ground.