15) When an object is dropped from a height of 314 feet, its height can be found using the equation. h=-162 +314 where t is seconds after the object is released. How long does it take the object to reach height 250?
15) When an object is dropped from a height of 314 feet, its height can be found using the equation. h=-162 +314 where t is seconds after the object is released. How long does it take the object to reach height 250?
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
![**Problem Statement:**
When an object is dropped from a height of 314 feet, its height can be found using the equation:
\[ h = -16t^2 + 314 \]
where \( t \) is the time in seconds after the object is released. How long does it take the object to reach a height of 250 feet?
**Explanation:**
This problem involves quadratic equations to determine the time it takes for an object in free fall to reach a certain height. The given equation is a standard form of a quadratic equation representing the height \( h \) of the object as a function of time \( t \). The constant 314 represents the initial height from which the object is dropped. The term \(-16t^2\) accounts for the acceleration due to gravity, which is approximately \(-32 \text{ feet/second}^2\) (divided by 2 in the equation).
To find the time \( t \) when the object's height \( h \) is 250 feet, substitute 250 for \( h \) in the equation and solve for \( t \):
\[ 250 = -16t^2 + 314 \]
This equation can be rearranged and solved using standard algebraic methods for quadratic equations, such as factoring, completing the square, or the quadratic formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b0597e7-a8c4-4734-b894-44b105c8693d%2Fb50daa2f-66b4-402b-aefb-6e1083165626%2F9elkgrg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
When an object is dropped from a height of 314 feet, its height can be found using the equation:
\[ h = -16t^2 + 314 \]
where \( t \) is the time in seconds after the object is released. How long does it take the object to reach a height of 250 feet?
**Explanation:**
This problem involves quadratic equations to determine the time it takes for an object in free fall to reach a certain height. The given equation is a standard form of a quadratic equation representing the height \( h \) of the object as a function of time \( t \). The constant 314 represents the initial height from which the object is dropped. The term \(-16t^2\) accounts for the acceleration due to gravity, which is approximately \(-32 \text{ feet/second}^2\) (divided by 2 in the equation).
To find the time \( t \) when the object's height \( h \) is 250 feet, substitute 250 for \( h \) in the equation and solve for \( t \):
\[ 250 = -16t^2 + 314 \]
This equation can be rearranged and solved using standard algebraic methods for quadratic equations, such as factoring, completing the square, or the quadratic formula.
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