Problem

Interpret \(h(t)=-16(t-1)(t-5)\) for \(1\le~t\le~5\). Derive each zero from its factor, attach the ground-event meaning, enforce the domain, compute elapsed flight time, and compare with the displayed answer diagram.

Big Picture

What this problem is really about

In a height model, zeros mark times when the object is at ground level. We’ll set each visible time factor equal to zero, check both times against the restricted domain, label the earlier and later ground events, and subtract the start time from the end time to obtain elapsed flight time.

Answer choices

Choose your path.

Preview only

Factors t − 1 and t − 5 give zeros 1 and 5 seconds. Both are in the domain, and the factors represent the rocket's maximum heights rather than ground times.

Factors t − 1 and t − 5 give zeros 1 and 5 seconds. Both are in the domain, and the flight duration is 5 seconds because the later zero is 5.

Factor t − 1 gives zero t = 1 second, the ground start; factor t − 5 gives zero t = 5 seconds, the ground return. Both zeros are in the domain, so the flight lasts 4 seconds.

Factor t − 1 gives zero t = −1 second and factor t − 5 gives zero t = −5 seconds. Neither is in the domain, so the rocket has no ground times.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Interpret \(h(t)=-16(t-1)(t-5)\) for \(1\le~t\le~5\). Derive each zero from its factor, attach the ground-event meaning, enforce the domain, compute elapsed flight time, and compare with the displayed answer diagram.

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.