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)= - 15.6t+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)= - 15.6t+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
Help
![**Problem:**
The velocity (in feet/second) of a projectile \( t \) seconds after it is launched from a height of 10 feet is given by \( v(t) = -15.6t + 147 \). Approximate its height after 3 seconds using 6 rectangles.
**Solution:**
First, we need to use the given velocity function to approximate the height of the projectile after 3 seconds. The velocity function is \( v(t) = -15.6t + 147 \).
To approximate the height after 3 seconds using 6 rectangles, we need to use the concept of Riemann sums where the number of rectangles (n) is 6.
Below are the steps to proceed:
1. **Divide the interval \([0, 3]\) into 6 subintervals:**
- The width of each subinterval, \(\Delta t\) = \(\frac{3 - 0}{6} = 0.5\) seconds.
2. **Calculate the midpoints of each subinterval:**
- For each subinterval, the midpoint, \( t_i \), can be calculated as follows:
- \( t_1 = \frac{0 + 0.5}{2} = 0.25 \)
- \( t_2 = \frac{0.5 + 1.0}{2} = 0.75 \)
- \( t_3 = \frac{1.0 + 1.5}{2} = 1.25 \)
- \( t_4 = \frac{1.5 + 2.0}{2} = 1.75 \)
- \( t_5 = \frac{2.0 + 2.5}{2} = 2.25 \)
- \( t_6 = \frac{2.5 + 3.0}{2} = 2.75 \)
3. **Evaluate the velocity function at each midpoint:**
- \( v(t_1) = v(0.25) = -15.6(0.25) + 147 \)
- \( v(t_2) = v(0.75) = -15.6(0.75) + 147 \)
- \( v(t_3) = v(1.25) = -15.6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f26cfff-a5a0-4f1a-b4dd-ba875949e336%2F560fa4a9-a94b-4e9c-8030-6009a67f262d%2Fdznk86a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
The velocity (in feet/second) of a projectile \( t \) seconds after it is launched from a height of 10 feet is given by \( v(t) = -15.6t + 147 \). Approximate its height after 3 seconds using 6 rectangles.
**Solution:**
First, we need to use the given velocity function to approximate the height of the projectile after 3 seconds. The velocity function is \( v(t) = -15.6t + 147 \).
To approximate the height after 3 seconds using 6 rectangles, we need to use the concept of Riemann sums where the number of rectangles (n) is 6.
Below are the steps to proceed:
1. **Divide the interval \([0, 3]\) into 6 subintervals:**
- The width of each subinterval, \(\Delta t\) = \(\frac{3 - 0}{6} = 0.5\) seconds.
2. **Calculate the midpoints of each subinterval:**
- For each subinterval, the midpoint, \( t_i \), can be calculated as follows:
- \( t_1 = \frac{0 + 0.5}{2} = 0.25 \)
- \( t_2 = \frac{0.5 + 1.0}{2} = 0.75 \)
- \( t_3 = \frac{1.0 + 1.5}{2} = 1.25 \)
- \( t_4 = \frac{1.5 + 2.0}{2} = 1.75 \)
- \( t_5 = \frac{2.0 + 2.5}{2} = 2.25 \)
- \( t_6 = \frac{2.5 + 3.0}{2} = 2.75 \)
3. **Evaluate the velocity function at each midpoint:**
- \( v(t_1) = v(0.25) = -15.6(0.25) + 147 \)
- \( v(t_2) = v(0.75) = -15.6(0.75) + 147 \)
- \( v(t_3) = v(1.25) = -15.6
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
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,
