A rock falls from a tower that is 192 feet high. As it is falling, its height its height is given by the formula: h = 192 - 16t². How many seconds (to the nearest tenths) will it take for the rock to hit the ground? It will take about 2.3 seconds for the rock to hit the ground. It will take about 3.5 seconds for the rock to hit the ground. O It will take about 4.1 seconds for the rock to hit the ground. It will take about 13.9 seconds for the rock to hit the ground.
A rock falls from a tower that is 192 feet high. As it is falling, its height its height is given by the formula: h = 192 - 16t². How many seconds (to the nearest tenths) will it take for the rock to hit the ground? It will take about 2.3 seconds for the rock to hit the ground. It will take about 3.5 seconds for the rock to hit the ground. O It will take about 4.1 seconds for the rock to hit the ground. It will take about 13.9 seconds for the rock to hit the ground.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Question:**
A rock falls from a tower that is 192 feet high. As it is falling, its height is given by the formula: \( h = 192 - 16t^2 \). How many seconds (to the nearest tenths) will it take for the rock to hit the ground?
**Options:**
- ○ It will take about 2.3 seconds for the rock to hit the ground.
- ○ It will take about 3.5 seconds for the rock to hit the ground.
- ○ It will take about 4.1 seconds for the rock to hit the ground.
- ○ It will take about 13.9 seconds for the rock to hit the ground.
The given formula describes the height \( h \) (in feet) of the rock as a function of time \( t \) (in seconds). To find the time it takes for the rock to hit the ground, we need to determine when the height \( h \) becomes zero.
By setting the height formula \( h = 192 - 16t^2 \) equal to 0, we solve for \( t \):
\[ 192 - 16t^2 = 0 \]
\[ 192 = 16t^2 \]
\[ t^2 = \frac{192}{16} \]
\[ t^2 = 12 \]
\[ t = \sqrt{12} \]
\[ t \approx 3.5 \]
Therefore, the rock will hit the ground in approximately 3.5 seconds. The correct answer is:
- ○ It will take about 3.5 seconds for the rock to hit the ground.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70fe4f99-9e69-4bef-afe6-80d54e8903ee%2F1812d113-ba37-40d7-929d-80b80af2d5fa%2Fnow1y6w_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
A rock falls from a tower that is 192 feet high. As it is falling, its height is given by the formula: \( h = 192 - 16t^2 \). How many seconds (to the nearest tenths) will it take for the rock to hit the ground?
**Options:**
- ○ It will take about 2.3 seconds for the rock to hit the ground.
- ○ It will take about 3.5 seconds for the rock to hit the ground.
- ○ It will take about 4.1 seconds for the rock to hit the ground.
- ○ It will take about 13.9 seconds for the rock to hit the ground.
The given formula describes the height \( h \) (in feet) of the rock as a function of time \( t \) (in seconds). To find the time it takes for the rock to hit the ground, we need to determine when the height \( h \) becomes zero.
By setting the height formula \( h = 192 - 16t^2 \) equal to 0, we solve for \( t \):
\[ 192 - 16t^2 = 0 \]
\[ 192 = 16t^2 \]
\[ t^2 = \frac{192}{16} \]
\[ t^2 = 12 \]
\[ t = \sqrt{12} \]
\[ t \approx 3.5 \]
Therefore, the rock will hit the ground in approximately 3.5 seconds. The correct answer is:
- ○ It will take about 3.5 seconds for the rock to hit the ground.
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