Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Physics Problem on Projectile Motion
#### Problem Statement:
A rock was thrown with an upward velocity of 12 meters per second from a cliff that is 45 meters high. What is the height of the rock above the cliff after \( t \) seconds?
The height of the rock \( n(t) \) after \( t \) seconds can be described by the equation:
\[ n(t) = -4.9t^2 + 12t + 45 \]
#### Explanation:
- The term \(-4.9t^2\) represents the acceleration due to gravity, which is approximately \(9.8 \, \text{m/s}^2\) acting in the downward direction.
- The term \(12t\) represents the initial upward velocity of the rock.
- The constant term \(45\) represents the initial height of the cliff from which the rock was thrown.
Students can use this quadratic equation to calculate the height of the rock at any given time \( t \). For instance, by substituting different values of \( t \), you can determine the rock’s height at various points in time until it reaches the ground again.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87c6590a-3759-4f4e-bb57-64d6c25bd8a3%2Fb3ceb730-81f9-4a88-9d59-787f3cbcdd70%2F247uen4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Physics Problem on Projectile Motion
#### Problem Statement:
A rock was thrown with an upward velocity of 12 meters per second from a cliff that is 45 meters high. What is the height of the rock above the cliff after \( t \) seconds?
The height of the rock \( n(t) \) after \( t \) seconds can be described by the equation:
\[ n(t) = -4.9t^2 + 12t + 45 \]
#### Explanation:
- The term \(-4.9t^2\) represents the acceleration due to gravity, which is approximately \(9.8 \, \text{m/s}^2\) acting in the downward direction.
- The term \(12t\) represents the initial upward velocity of the rock.
- The constant term \(45\) represents the initial height of the cliff from which the rock was thrown.
Students can use this quadratic equation to calculate the height of the rock at any given time \( t \). For instance, by substituting different values of \( t \), you can determine the rock’s height at various points in time until it reaches the ground again.
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