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.

Question

A 2-column table with 6 rows titled Height of Coconut over Time. The first column is labeled t with entries 0, 1, 2, 3, 4, 5. The second column is labeled h(t) with entries 210, 194, 146, 66, negative 46, negative 190.
Which statement is true?

The initial height of the coconut is 190 feet.
The coconut will hit the ground between 4 and 5 seconds after it was dropped.
The values of h(t) when t = 4 and 5 should be 0.
The maximum height of the coconut was 1 second after it was dropped.

Answer 1

Let's analyze the provided statements based on the table of values:

1. The initial height of the coconut is 190 feet.

   • This is false. The initial height when \( t = 0 \) is 210 feet.

2. The coconut will hit the ground between 4 and 5 seconds after it was dropped.

   • This is true. At \( t = 4 \), the height \( h(4) = -46 \), and at \( t = 5 \), the height \( h(5) = -190 \). The height becomes negative at these times, indicating that the coconut has already hit the ground before reaching 0 feet, but it certainly landed somewhere between 4 and 5 seconds.

3. The values of h(t) when t = 4 and 5 should be 0.

   • This is false. The values for \( h(t) \) are negative at those time points, which indicates the coconut has already hit the ground and is below the ground level.

4. The maximum height of the coconut was 1 second after it was dropped.

   • This is false. The maximum height is at \( t = 0 \), which is 210 feet.

Given the analysis, the only true statement is:

The coconut will hit the ground between 4 and 5 seconds after it was dropped.