Final answer:
To determine the time for the ball to hit the ground, substitute the given values into the quadratic formula and solve for t, disregarding the negative value since time cannot be negative.
Step-by-step explanation:
To find the time it takes for the ball to hit the ground when thrown upwards from a height of 15 ft. with an initial velocity of 5 ft/s, you can use the quadratic formula to solve for time t in the equation h(f) = -16t² + (initial velocity)t + (initial height). In your case, the formula becomes:
0 = -16t² + 5t + 15.
Using the quadratic formula, t = (-b ± √(b²-4ac))/(2a), you'll find the two possible times when the ball will be at ground level. Ensure that the negative time is disregarded as it does not fit the context of the problem, and use only the positive time.
The ball will hit the ground after the positive value of t seconds, which is found after calculating the quadratic formula.