To find the height of the rocket at a given time, we can plug the value of $t$ (time in seconds) into the equation:

$h = -4.9t^2 + 328t + 409$

1. Height of the rocket after 3 seconds:

Substitute $t = 3$ into the equation:

$h = -4.9(3)^2 + 328(3) + 409$

Calculating step-by-step: $3^2 = 9$ $-4.9 \times 9 = -44.1$ $328 \times 3 = 984$

So, the height after 3 seconds is: $h = -44.1 + 984 + 409 = 1348.9 \text{ meters}$

Therefore, the rocket is 1,348.9 meters above sea level after 3 seconds.

2. Height of the rocket at launch (initial height):

At $t = 0$, the equation simplifies to:

$h = -4.9(0)^2 + 328(0) + 409 = 409$

Thus, the initial height of the rocket when launched was 409 meters.

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Do you want details or have any questions?

Here are some related questions:

1. What would be the rocket's height after 10 seconds?
2. When does the rocket reach its maximum height?
3. What is the maximum height of the rocket?
4. How long does it take for the rocket to hit the ground?
5. Can we determine the velocity of the rocket at any time $t$?

Tip: When dealing with quadratic equations in physics, the coefficient of $t^2$ represents the acceleration (due to gravity in this case), while the coefficient of $t$ represents the initial velocity.