The function $M(t)=-4.87 t^{2}+18.75 t$ is used to model the height of an object projected in the air, where $h(t)$ is the height in meters and $t$ is the time in seconds. What are the domain and range of the function $h(t)$ ? Round values to the nearest hundredth.

Step 1 ：Given the function \(h(t) = -4.87t^2 + 18.75t\), where \(h(t)\) is the height in meters and \(t\) is the time in seconds.

Step 2 ：Find the vertex of the parabola to determine the maximum height: \(t_{vertex} = \frac{-b}{2a} = \frac{-18.75}{2(-4.87)} = 1.93\) (rounded to the nearest hundredth).

Step 3 ：Plug \(t_{vertex}\) back into the function to find the maximum height: \(h(1.93) = -4.87(1.93)^2 + 18.75(1.93) = 18.05\) meters (rounded to the nearest hundredth).

Step 4 ：Solve the equation for \(t\) when \(h(t) = 0\) to find when the object hits the ground: \(-4.87t^2 + 18.75t = 0\).

Step 5 ：Factor out \(t\) to get \(t(-4.87t + 18.75) = 0\).

Step 6 ：The two possible values for \(t\) are \(0\) and \(\frac{18.75}{4.87} = 3.85\) seconds (rounded to the nearest hundredth).

Step 7 ：Final Answer: The domain of the function \(h(t)\) is \(\boxed{[0, 3.85]}\) seconds (rounded to the nearest hundredth), and the range of the function is \(\boxed{[0, 18.05]}\) meters (rounded to the nearest hundredth).