Final answer:
To find the time t when h(t) = 0 for the equation h(t) = -16t^2 + h0, solve the quadratic equation and discard the negative time solution, retaining only the positive one.
Step-by-step explanation:
To solve for t when h(t) = 0 in the equation h(t) = -16t^2 + h0, where h0 is the initial height, we look for the roots of the quadratic equation. Given that we ignore negative time values because they are not physically meaningful in this context, we are interested in finding the positive value of t.
Using the quadratic formula or by factoring, if possible, we find the values of t that satisfy the equation. In problems similar to this, if we have a quadratic equation like t^2 + 10t - 2000 = 0, we would solve for t using the quadratic formula, yielding two solutions, one positive and one negative. We discard the negative solution and use the positive one as the answer.
In the provided examples, negative times are consistently disregarded as they imply events before the start of motion. Therefore, for the given function h(t) = -16t^2 + h0, we should solve for t, keep the positive solution, and discard the negative one.