Question 4 A diver followed a path defined by $h(t)=-4.9 t^{2}+3 t+10$ in her dive, where $t$ is the time, in seconds, and $h$ represents her height above the water, in metres.
a) What was the maximum height the diver reached?
[2]

Step 1 ：The maximum height the diver reached can be found by finding the maximum point of the quadratic function \(h(t)=-4.9 t^{2}+3 t+10\). This can be done by finding the vertex of the parabola.

Step 2 ：The vertex of the parabola is given by the formula \(t = -\frac{b}{2a}\) where \(a\) and \(b\) are the coefficients of \(t^2\) and \(t\) respectively.

Step 3 ：Substituting the values of \(a\) and \(b\) into the formula, we get \(t = -\frac{3}{2*-4.9} = 0.3061224489795918\).

Step 4 ：Once we have the value of \(t\) at the vertex, we can substitute it back into the function to find the maximum height.

Step 5 ：Substituting \(t = 0.3061224489795918\) into the function \(h(t)=-4.9 t^{2}+3 t+10\), we get \(h = 10.4591836734694\).

Step 6 ：Final Answer: The maximum height the diver reached is approximately \(\boxed{10.46}\) metres.