The velocity (in feet/second) of a projectile t seconds after it is launched from a height of 10 feet is given by v(t)= - 15.2t+146. Approximate its height after 3 seconds using 6 rectangles. It is approximatley feet. (Round final answer to nearest tenth. Do NOT round until the final answer.) roj
The velocity (in feet/second) of a projectile t seconds after it is launched from a height of 10 feet is given by v(t)= - 15.2t+146. Approximate its height after 3 seconds using 6 rectangles. It is approximatley feet. (Round final answer to nearest tenth. Do NOT round until the final answer.) roj
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
100%
Help
![**Problem Statement:**
The velocity (in feet/second) of a projectile \( t \) seconds after it is launched from a height of 10 feet is given by:
\[ v(t) = -15.2t + 146 \]
Approximate its height after 3 seconds using 6 rectangles.
---
**Solution Steps:**
* The height of the projectile can be found by integrating the velocity function \( v(t) \).
* To approximate this height at \( t = 3 \) seconds, we will use the method of Riemann sums with 6 rectangles.
* Given the velocity function, \( v(t) = -15.2t + 146 \), over the interval from \( t = 0 \) to \( t = 3 \) seconds, we will divide this interval into 6 subintervals.
* The width of each subinterval (rectangle) is:
\[ \Delta t = \frac{3 - 0}{6} = 0.5 \text{ seconds} \]
* For each subinterval \( [t_i, t_{i+1}] \), the height of the rectangle can be approximated using the left endpoint \( t_i \):
\[ \text{Height}_{i} \approx v(t_i) \]
* Summing the areas of these rectangles gives an approximation of the integral of \( v(t) \) over the interval \( [0, 3] \).
---
**Calculation:**
1. Divide the interval \( [0, 3] \) into 6 equal parts:
\[ t = \{0, 0.5, 1, 1.5, 2, 2.5, 3\} \]
2. Calculate \( v(t_i) \) for \( t_i = 0, 0.5, 1, 1.5, 2, 2.5 \):
\[ v(0) = -15.2(0) + 146 = 146 \]
\[ v(0.5) = -15.2(0.5) + 146 = 138.4 \]
\[ v(1) = -15.2(1) + 146 = 130.8 \]
\[ v(1.5) = -15.2(1.5) + 146 = 123.2 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4381201-1e37-4b9b-b7bd-26ff22647909%2Fb76dbc31-02f8-43a1-b6b4-c1e855db6dbb%2Fvf8voew_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The velocity (in feet/second) of a projectile \( t \) seconds after it is launched from a height of 10 feet is given by:
\[ v(t) = -15.2t + 146 \]
Approximate its height after 3 seconds using 6 rectangles.
---
**Solution Steps:**
* The height of the projectile can be found by integrating the velocity function \( v(t) \).
* To approximate this height at \( t = 3 \) seconds, we will use the method of Riemann sums with 6 rectangles.
* Given the velocity function, \( v(t) = -15.2t + 146 \), over the interval from \( t = 0 \) to \( t = 3 \) seconds, we will divide this interval into 6 subintervals.
* The width of each subinterval (rectangle) is:
\[ \Delta t = \frac{3 - 0}{6} = 0.5 \text{ seconds} \]
* For each subinterval \( [t_i, t_{i+1}] \), the height of the rectangle can be approximated using the left endpoint \( t_i \):
\[ \text{Height}_{i} \approx v(t_i) \]
* Summing the areas of these rectangles gives an approximation of the integral of \( v(t) \) over the interval \( [0, 3] \).
---
**Calculation:**
1. Divide the interval \( [0, 3] \) into 6 equal parts:
\[ t = \{0, 0.5, 1, 1.5, 2, 2.5, 3\} \]
2. Calculate \( v(t_i) \) for \( t_i = 0, 0.5, 1, 1.5, 2, 2.5 \):
\[ v(0) = -15.2(0) + 146 = 146 \]
\[ v(0.5) = -15.2(0.5) + 146 = 138.4 \]
\[ v(1) = -15.2(1) + 146 = 130.8 \]
\[ v(1.5) = -15.2(1.5) + 146 = 123.2 \]
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 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning