The equation h = 16t² can be used to estimate the height (h) an object is dropped from given the time in seconds (s) it falls. M a. If you dropped a rock off a cliff and it took 2.5 seconds to hit, how tall is the cliff? b. If a cliff were 2,500' tall, how long would it take?
The equation h = 16t² can be used to estimate the height (h) an object is dropped from given the time in seconds (s) it falls. M a. If you dropped a rock off a cliff and it took 2.5 seconds to hit, how tall is the cliff? b. If a cliff were 2,500' tall, how long would it take?
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,...
Related questions
Question
![### Estimating the Height of a Falling Object
The equation \( h = 16t^2 \) can be used to estimate the height (h) an object is dropped from, given the time in seconds (t) it falls.
#### Exercises:
1. **Scenario A:**
If you dropped a rock off a cliff and it took 2.5 seconds to hit the ground, how tall is the cliff?
2. **Scenario B:**
If a cliff were 2,500 feet tall, how long would it take for a rock to hit the ground if dropped from the top?
---
### Detailed Explanation
The equation \( h = 16t^2 \) helps us understand the relationship between the height and the time it takes for an object to fall. Here's what each part of the equation represents:
- **h**: Height in feet
- **t**: Time in seconds
- **16**: A constant that represents half the acceleration due to gravity (assuming the object is falling freely under gravity with no air resistance).
#### Example Solutions:
1. **Solving Scenario A:**
- Given: \( t = 2.5 \) seconds
- Substitute the given time into the equation:
\[
h = 16 \times (2.5)^2
\]
- Calculate:
\[
h = 16 \times 6.25 = 100 \text{ feet}
\]
- **Answer:** The cliff is 100 feet tall.
2. **Solving Scenario B:**
- Given: \( h = 2500 \) feet
- Use the equation and solve for t:
\[
2500 = 16t^2
\]
- Rearrange for t:
\[
t^2 = \frac{2500}{16} = 156.25
\]
- Calculate the square root to find t:
\[
t = \sqrt{156.25} = 12.5 \text{ seconds}
\]
- **Answer:** It would take 12.5 seconds for the rock to hit the ground.
By applying the formula and solving these exercises, you gain a better understanding of how to estimate the height of a cliff or the time an object takes to fall, given specific conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94589190-d7d8-41be-9c6e-d2d51b756765%2F563ad7bc-752b-4bb3-a8af-0e5a51c4a155%2F7rp89j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Estimating the Height of a Falling Object
The equation \( h = 16t^2 \) can be used to estimate the height (h) an object is dropped from, given the time in seconds (t) it falls.
#### Exercises:
1. **Scenario A:**
If you dropped a rock off a cliff and it took 2.5 seconds to hit the ground, how tall is the cliff?
2. **Scenario B:**
If a cliff were 2,500 feet tall, how long would it take for a rock to hit the ground if dropped from the top?
---
### Detailed Explanation
The equation \( h = 16t^2 \) helps us understand the relationship between the height and the time it takes for an object to fall. Here's what each part of the equation represents:
- **h**: Height in feet
- **t**: Time in seconds
- **16**: A constant that represents half the acceleration due to gravity (assuming the object is falling freely under gravity with no air resistance).
#### Example Solutions:
1. **Solving Scenario A:**
- Given: \( t = 2.5 \) seconds
- Substitute the given time into the equation:
\[
h = 16 \times (2.5)^2
\]
- Calculate:
\[
h = 16 \times 6.25 = 100 \text{ feet}
\]
- **Answer:** The cliff is 100 feet tall.
2. **Solving Scenario B:**
- Given: \( h = 2500 \) feet
- Use the equation and solve for t:
\[
2500 = 16t^2
\]
- Rearrange for t:
\[
t^2 = \frac{2500}{16} = 156.25
\]
- Calculate the square root to find t:
\[
t = \sqrt{156.25} = 12.5 \text{ seconds}
\]
- **Answer:** It would take 12.5 seconds for the rock to hit the ground.
By applying the formula and solving these exercises, you gain a better understanding of how to estimate the height of a cliff or the time an object takes to fall, given specific conditions.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education