Final answer:
To find when a ball thrown upward reaches a certain height, we use its height-time equation, set it equal to the given height, and solve for time using methods such as the quadratic formula. There will generally be two times, one during ascent and one during descent; the first positive time is usually the one sought.
Step-by-step explanation:
The question asks us to determine when the height of a ball, thrown upward, will be at a specific undisclosed height (presumably given in class but omitted in the question).
The height s of the ball as a function of time t can be modeled by a quadratic equation: s(t) = -16t² + 70t + 5. To find the time t when the ball reaches a certain height, we would set the equation s(t) equal to that height and solve for t using the quadratic formula or another appropriate method of solving quadratic equations.
According to the provided reference information, the ball reaches a particular height at two distinct times during its flight: once while ascending and once while descending. Since we are usually interested in the first occurrence, we usually take the first positive time from the solutions provided by the quadratic formula.
For example, if the specific height given was 10 feet, and if using the quadratic formula or another solving method gave us t = 3.79 s and t = 0.54 s, these would be the times the ball is at 10 feet on its way up and down, respectively. In solving a problem like this, we would probably be asked for both times. However, if we were only interested in the first time the ball reaches this height, we would select t = 0.54 s.