Final answer:
To calculate the height of the rocket 2 seconds after launch, substitute x=2 into the provided function F(x) and solve. The height is determined to be 308 meters.
Step-by-step explanation:
To determine the height of the rocket 2 seconds after launch, we need to evaluate the given quadratic function at x=2. The height function of a projectile in motion is often given by an equation of the form f(x) = ax² + bx + c, where x represents time in seconds.
The question provides us with a function: F(x) = -16x² + 96x + 180. To find the height at x=2, we substitute 2 for x in the function:
F(2) = -16(2)² + 96(2) + 180
= -16(4) + 192 + 180
= -64 + 192 + 180
= 308.
Therefore, the height of the rocket 2 seconds after it was launched is 308 meters.