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)= - 15.4t + 147. 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.)
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)= - 15.4t + 147. 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.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Help
![**Projectile Motion Approximation Using Rectangles**
The velocity (in feet/second) of a projectile \( t \) seconds after it is launched from a height of 10 feet is given by \( v(t) = -15.4t + 147 \). To approximate its height after 3 seconds using 6 rectangles, follow these steps:
1. Divide the interval [0,3] into 6 equal subintervals. Each subinterval will have a width of \( \Delta t = \frac{3-0}{6} = 0.5 \) seconds.
2. Calculate the velocity, \( v(t) \), at the right endpoint of each subinterval.
3. Use the velocity values to approximate the height by summing the areas of the rectangles.
Calculate each rectangle area:
- For the first interval \([0, 0.5]\):
\( v(0.5) = -15.4(0.5) + 147 \)
- For the second interval \([0.5, 1.0]\):
\( v(1.0) = -15.4(1.0) + 147 \)
- Continue this process for \( t = 1.5, \ 2.0, \ 2.5, \ and \ 3.0 \).
Summing these areas provides an approximate total displacement, which, when added to the initial height of 10 feet, gives the approximate height after 3 seconds.
**It is approximately \_\_\_\_ feet.**
*(Round the final answer to the nearest tenth. Do NOT round until the final answer.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ed63b8c-5f2a-459c-b7ed-e6789166686d%2F3b446a46-426a-4257-8c4f-7122ac67c6b6%2Fb6gx2q8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Projectile Motion Approximation Using Rectangles**
The velocity (in feet/second) of a projectile \( t \) seconds after it is launched from a height of 10 feet is given by \( v(t) = -15.4t + 147 \). To approximate its height after 3 seconds using 6 rectangles, follow these steps:
1. Divide the interval [0,3] into 6 equal subintervals. Each subinterval will have a width of \( \Delta t = \frac{3-0}{6} = 0.5 \) seconds.
2. Calculate the velocity, \( v(t) \), at the right endpoint of each subinterval.
3. Use the velocity values to approximate the height by summing the areas of the rectangles.
Calculate each rectangle area:
- For the first interval \([0, 0.5]\):
\( v(0.5) = -15.4(0.5) + 147 \)
- For the second interval \([0.5, 1.0]\):
\( v(1.0) = -15.4(1.0) + 147 \)
- Continue this process for \( t = 1.5, \ 2.0, \ 2.5, \ and \ 3.0 \).
Summing these areas provides an approximate total displacement, which, when added to the initial height of 10 feet, gives the approximate height after 3 seconds.
**It is approximately \_\_\_\_ feet.**
*(Round the final answer to the nearest tenth. Do NOT round until the final answer.)*
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
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
