Question

marlena created a table of values representing the height in feet, h(t), of a coconut falling to the hard ground with a height of 0 feet, collected over t seconds. assume the coconut does not bounce and rests on the ground when it lands. which statement is true? the initial height of the coconut is 190 feet the coconut will hit the ground between seconds after it was dropped. the values of h(t) when t = 4 and 5 show the maximum height of the coconut after it was dropped. height of coconut over time

Explanation:

Step1: Analyze the initial height

When \(t = 0\), \(h(0)=210\) feet. So the initial height is 210 feet, not 190 feet.

Step2: Check when the coconut hits the ground

The coconut hits the ground when \(h(t)=0\). At \(t = 3\), \(h(3)=66\); at \(t = 4\), \(h(4)=- 46\). Since the function is continuous (assuming it is a polynomial - like fall, as it's a physical motion of falling), by the Intermediate Value Theorem, there is a \(t\) value between \(3\) and \(4\) such that \(h(t)=0\).

Step3: Analyze the values at \(t = 4\) and \(t = 5\)

The values \(h(4)=-46\) and \(h(5)=-190\) are both negative. They do not "show" a particular non - negative trend (the problem statement about what they "show" is not clearly defined in a correct way here, but the key is the ground - hitting analysis).

Step4: Analyze the maximum height

The maximum height occurs at \(t = 0\) (initial height) since the coconut is falling.

Answer:

The coconut will hit the ground between 3 and 4 seconds after it was dropped.