A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 90t, at which time the fuel is exhausted and it becomes a freely "falling" body. Eighteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -11 ft/s in 5 seconds. The rocket then "floats" to the ground at that rate. (a) Determine the position function s and the velocity function v (for all times t). 45? if 0sts 3 405 if 3 26 | 153 if 0sts 3 405 if 3 26
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 90t, at which time the fuel is exhausted and it becomes a freely "falling" body. Eighteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -11 ft/s in 5 seconds. The rocket then "floats" to the ground at that rate. (a) Determine the position function s and the velocity function v (for all times t). 45? if 0sts 3 405 if 3 26 | 153 if 0sts 3 405 if 3 26
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
![Transcript for Educational Website:
---
**Rocket Flight Analysis:**
(b) At what time does the rocket reach its maximum height?
- **Answer Box:** [ 0 ] **s** [Incorrect]
What is that height? (Round your answer to the nearest integer.)
- **Answer Box:** [ 0 ] **ft** [Incorrect]
(c) At what time does the rocket land? (Round your answer to one decimal place.)
- **Answer Box:** [ 0 ] **s** [Incorrect]
**Need Help?**
- **Read It** [Button]
---
This exercise appears to assess understanding of a rocket's flight path, focusing on identifying the maximum height achieved, the time at which this occurs, and when the rocket lands. Each question has an answer box with a placeholder value of 0, indicating incorrect answers. A help option is also available.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7f0b2bf-1c33-403f-99a4-8741414e9a7b%2Fddde5576-35ae-4c6f-9df9-d7f68377c68a%2F1j95oa9_processed.png&w=3840&q=75)
Transcribed Image Text:Transcript for Educational Website:
---
**Rocket Flight Analysis:**
(b) At what time does the rocket reach its maximum height?
- **Answer Box:** [ 0 ] **s** [Incorrect]
What is that height? (Round your answer to the nearest integer.)
- **Answer Box:** [ 0 ] **ft** [Incorrect]
(c) At what time does the rocket land? (Round your answer to one decimal place.)
- **Answer Box:** [ 0 ] **s** [Incorrect]
**Need Help?**
- **Read It** [Button]
---
This exercise appears to assess understanding of a rocket's flight path, focusing on identifying the maximum height achieved, the time at which this occurs, and when the rocket lands. Each question has an answer box with a placeholder value of 0, indicating incorrect answers. A help option is also available.
![A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is \( a(t) = 90t \), at which time the fuel is exhausted and it becomes a freely "falling" body. Eighteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to \(-11\) ft/s in 5 seconds. The rocket then "floats" to the ground at that rate.
(a) Determine the position function \( s \) and the velocity function \( v \) (for all times \( t \)).
### Velocity Function: \( v(t) \)
\[
v(t) =
\begin{cases}
45t^2 & \text{if } 0 \leq t \leq 3 \\
405 & \text{if } 3 < t \leq 21 \\
(blank) & \text{if } 21 < t \leq 26 \\
(blank) & \text{if } t > 26
\end{cases}
\]
### Position Function: \( s(t) \)
\[
s(t) =
\begin{cases}
15t^3 & \text{if } 0 \leq t \leq 3 \\
405t & \text{if } 3 < t \leq 21 \\
(blank) & \text{if } 21 < t \leq 26 \\
(blank) & \text{if } t > 26
\end{cases}
\]
### Diagram Explanation
The diagram consists of two equations, one for velocity and one for position, which describe the motion of a model rocket. Each equation has different expressions based on time intervals:
- For both functions, specific expressions are provided for \( 0 \leq t \leq 3 \) and \( 3 < t \leq 21 \).
- The expressions for the intervals \( 21 < t \leq 26 \) and \( t > 26 \) are not filled in.
The green check marks indicate correct equations for defined intervals, while the red crosses suggest that there is additional information needed or the function may not be applicable as stated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7f0b2bf-1c33-403f-99a4-8741414e9a7b%2Fddde5576-35ae-4c6f-9df9-d7f68377c68a%2Fz0ls7tt_processed.png&w=3840&q=75)
Transcribed Image Text:A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is \( a(t) = 90t \), at which time the fuel is exhausted and it becomes a freely "falling" body. Eighteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to \(-11\) ft/s in 5 seconds. The rocket then "floats" to the ground at that rate.
(a) Determine the position function \( s \) and the velocity function \( v \) (for all times \( t \)).
### Velocity Function: \( v(t) \)
\[
v(t) =
\begin{cases}
45t^2 & \text{if } 0 \leq t \leq 3 \\
405 & \text{if } 3 < t \leq 21 \\
(blank) & \text{if } 21 < t \leq 26 \\
(blank) & \text{if } t > 26
\end{cases}
\]
### Position Function: \( s(t) \)
\[
s(t) =
\begin{cases}
15t^3 & \text{if } 0 \leq t \leq 3 \\
405t & \text{if } 3 < t \leq 21 \\
(blank) & \text{if } 21 < t \leq 26 \\
(blank) & \text{if } t > 26
\end{cases}
\]
### Diagram Explanation
The diagram consists of two equations, one for velocity and one for position, which describe the motion of a model rocket. Each equation has different expressions based on time intervals:
- For both functions, specific expressions are provided for \( 0 \leq t \leq 3 \) and \( 3 < t \leq 21 \).
- The expressions for the intervals \( 21 < t \leq 26 \) and \( t > 26 \) are not filled in.
The green check marks indicate correct equations for defined intervals, while the red crosses suggest that there is additional information needed or the function may not be applicable as stated.
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 4 steps with 5 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