Final answer:
The question involves using a quadratic equation to calculate the time it takes for a paintbrush to fall from a height of 6 feet. By setting the final height to 0 in the equation h = -16t² + h_0, and solving for t, we find the time it takes for the paintbrush to hit the ground.
Step-by-step explanation:
The student's question involves calculating the time it takes for a paintbrush to fall to the ground using a quadratic equation from the physics of free-fall motion. The given formula is h = -16t² + h_0, where h is the final height (which will be 0 when the paintbrush hits the ground), t is the time in seconds, and h_0 is the initial height in feet from which the object is dropped (in this case, 6 feet).
Setting h equal to 0 for when the paintbrush hits the ground and substituting in the initial height, we get 0 = -16t² + 6. Solving this equation for t involves rearranging the terms to 16t² = 6 and then solving for t by taking the square root of the result after dividing by 16. The positive root is taken because time cannot be negative. This yields the approximate time it takes for the paintbrush to hit the ground.