Question

a model rocket is launched into the air from ground level. the height, in feet, in feet, is modeled by p(x)=-16x²+32x, where x is the number of elapsed seconds. what is the total number of seconds the model rocket will be in the air?

Answer 1

The model rocket described by the quadratic equation p(x) = -16x² + 32x will be in the air for 2 seconds before it returns to ground level.

Step-by-step explanation:

The total number of seconds the model rocket will be in the air is determined by finding the roots of the height function p(x) = -16x² + 32x, which represents a quadratic equation. To find the time when the rocket returns to the ground (height equals zero), we set the equation to zero and solve for x.

0 = -16x² + 32x

This can be simplified by factoring out -16x:

-16x(x - 2) = 0

Setting each factor equal to zero gives us two solutions for x:

• x = 0 (at launch)
• x = 2 (when the rocket hits the ground)

The rocket will be in the air until x = 2 seconds, which is when it returns to ground level.