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The equation for the height of the toy rocket is given as:

\[
h = -4.9t^2 + 28.7t + 4.2
\]

To determine when the rocket hits the ground, we need to find when \( h = 0 \), which corresponds to solving the following quadratic equation:

\[
0 = -4.9t^2 + 28.7t + 4.2
\]

Let me solve this quadratic equation to find the value of \( t \) (time when the rocket hits the ground).The two solutions for the time when the rocket hits the ground are:

- \( t_1 \approx -0.14 \) (which we discard, as time cannot be negative)
- \( t_2 \approx 6.00 \) seconds

Thus, the toy rocket will hit the ground after approximately **6 seconds**.

Do you need more details, or do you have any questions?

Here are 5 related questions for practice:
1. What is the maximum height reached by the rocket?
2. At what time does the rocket reach its maximum height?
3. How would the trajectory change if the initial velocity were different?
4. What is the height of the rocket after 2 seconds?
5. How does air resistance affect the rocket's flight?

**Tip:** When solving quadratic equations, always check the discriminant to determine whether there are real or complex solutions.

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

Learn how to solve a real-world quadratic equation involving the height of a toy rocket. This problem focuses on projectile motion and the quadratic formula, helping students understand key concepts in Algebra and Physics. Suitable for students in Grades 9-10.

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