marfena created a table of values representing the height in feet, ( h(t) ), of a coconut falling to the 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 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.

Question

marfena created a table of values representing the height in feet, ( h(t) ), of a coconut falling to the 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 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.

Accepted Answer

# Brief Explanations:
- Initial height is at $t=0$: $h(0)=210$ feet, so first statement is false.
- Ground height is 0 feet. $h(t)$ goes negative between $t=3$ (66 ft) and $t=4$ (-46 ft), meaning it hits ground between 3 and 4 seconds, not 4 and 5—second statement false.
- $h(t)$ values at $t=4$ (-46) and $t=5$ (-190) are negative, not 0—third statement false.
- Maximum height occurs at $t=0$ (210 ft), not $t=1$ (194 ft)—fourth statement false.
- Wait, correction: The coconut hits ground when height transitions from positive to negative. At $t=3$, height is 66 ft (positive); $t=4$, -46 ft (negative). So it hits ground between 3 and 4 seconds? No, the options: Wait the second option says "between 4 and 5"—no. Wait the table: $t=0$ initial height 210, so first option says initial height 190—false. The second option: hits ground between 4 and5? No, between 3 and4. Third option: $h(t)=0$ between 4 and5? No, between3 and4. Fourth option: max height at $t=1$? No, max at $t=0$. Wait did I misread? Wait the options: The second statement is "The coconut will hit the ground between 4 and 5 seconds after it was dropped"—but table shows $t=3$ is 66, $t=4$ is -46, so it hits between 3 and4. So none? Wait no, maybe the question has a typo? Wait no, wait the options: Wait the first option says initial height 190—table $t=0$ is 210, so false. Second option: between4 and5—no. Third option: $h(t)=0$ between4 and5—no. Fourth option: max height at $t=1$—no. Wait wait, maybe I made a mistake: The max height is at $t=0$ (210), which is initial. So fourth option is false. So is there a correct option? Wait wait the table: $t=5$ is -190. No, wait maybe the question's options—wait the user's options: Let me recheck. The options are:
1. Initial height 190 (false, it's 210)
2. Hits ground between4 and5 (false, between3 and4)
3. $h(t)=0$ between4 and5 (false)
4. Max height at $t=1$ (false)

Wait this can't be. Wait no, maybe I misread the table: Is $t=0$ 210? Yes. $t=1$ 194, $t=2$146, $t=3$66, $t=4$-46, $t=5$-190. So the only possible? Wait no, maybe the question has a correct option: Wait the second option says between4 and5—no. Wait maybe the ground is not 0? No, the problem says "height of 0 feet" is ground. So the coconut hits ground when height is 0, which is between $t=3$ and $t=4$. So none of the options? But that's impossible. Wait wait, maybe the first option: initial height 190—no, $t=0$ is210. Oh wait, maybe the table was written wrong? No, the user's table is clear. Wait wait, maybe the question's options: Wait the user's options are four? Let me see: The user's question has four options:

- 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

Wait none are correct? But that's not possible. Wait wait, maybe the third option: "The values of h(t) when t=4 and 5 should be 0"—no, because it already hit ground before t=4. So no. Wait maybe the question has a typo, but according to the table, the only possible? Wait no, maybe I made a mistake. Wait the initial height is at t=0: 210, so first option is false. Max height is at t=0, so fourth is false. Hits ground between3 and4, so second is false. Third option: h(t) at t=4 and5 should be0—no. So is there a correct option? Wait wait, maybe the user's table was reversed? No. Oh wait, maybe the question's options: Wait the second option says between4 and5—no. So maybe the answer is none? But that's not possible. Wait wait, maybe I misread the question: "Assume the coconut does not bounce and rests on the ground when it lands." So when it hits ground, height stays 0. So after hitting ground, height is 0. So the coconut hits ground between t=3 and t=4, so after that, height should be0. So the values at t=4 and t=5 should be0, which is the third option. Oh! Oh right! Because once it hits ground (between3 and4), it rests there, so h(4) and h(5) should be0, not -46 and -190. So the third option is correct: "The values of h(t) when t=4 and 5 should be 0".

Ah! That's it. Because the problem says "Assume the coconut does not bounce and rests on the ground when it lands." So once it hits ground (height 0), it stays at 0. So the table's values for t=4 and t=5 (-46 and -190) are wrong—they should be 0. So the third option is correct.

# Answer:
The values of h(t) when t=4 and 5 should be 0

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