A toy rocket is launched from a 4.2 $\mathrm{m}$ high platform in such a way that its height, $\mathrm{h}$ (in meters), after $\mathrm{t}$ seconds is given by the equation $h=-4.9 t^{2}+28.7 t+4.2$ How long will it take for the rocket to hit the ground?

Step 1 ：Given the equation for the height of the rocket as \(h=-4.9 t^{2}+28.7 t+4.2\), we need to find the time \(t\) when the rocket hits the ground, i.e., when \(h=0\).

Step 2 ：This is a quadratic equation in the form \(at^2 + bt + c = 0\), where \(a = -4.9\), \(b = 28.7\), and \(c = 4.2\).

Step 3 ：We can solve this equation using the quadratic formula \(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

Step 4 ：Substituting the values of \(a\), \(b\), and \(c\) into the formula, we get two solutions for \(t\).

Step 5 ：However, since time cannot be negative, we discard the negative solution and keep the positive one.

Step 6 ：\(\boxed{6}\) seconds is the time it will take for the rocket to hit the ground.