Problem

For projectile height \(h(t)=-16t(t-4)~\text{feet}\) on \(0\le~t\le~4~\text{seconds}\), find the \(x\text{-}\text{intercepts}\) from the factors. State the intercept points, verify both times lie in the motion domain, and interpret each \(\text{zero}\text{-}\text{height}\) event.

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What this problem is really about

In a height model, time-axis intercepts mark inputs where the modeled height is zero. We’ll use the factors to find the candidate times, test each one against the motion domain, and then interpret the surviving zero-height events by their positions in the flight.

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t=0 and t=4 are times when the projectile has positive height.

The x-intercepts are height outputs 0 feet and 4 feet.

t=0 and t=4 are valid ground-level times: launch and landing.

t=−4, t=0, and t=4 are ground-level times, including a prelaunch event.

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For projectile height \(h(t)=-16t(t-4)~\text{feet}\) on \(0\le~t\le~4~\text{seconds}\), find the \(x\text{-}\text{intercepts}\) from the factors. State the intercept points, verify both times lie in the motion domain, and interpret each \(\text{zero}\text{-}\text{height}\) event.

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