On Earth, if you shoot a paper clip 96 ft/sec straight up into the air with a rubber band, the paper clip will be s(t) = 96t- 16t2 feet above your hand at t seconds after firing. A. Find ds. 96-32t d²s B. Find -32t C. Use the answer from part A to determine how long it takes the paper clip to reach a maximum height. D. When does the velocity of the particle reach -32 ft/sec? di2
On Earth, if you shoot a paper clip 96 ft/sec straight up into the air with a rubber band, the paper clip will be s(t) = 96t- 16t2 feet above your hand at t seconds after firing. A. Find ds. 96-32t d²s B. Find -32t C. Use the answer from part A to determine how long it takes the paper clip to reach a maximum height. D. When does the velocity of the particle reach -32 ft/sec? di2
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
please answer all parts and both questions with explanation. thank you!
![**Calculus Problems in Projectile Motion and Differentiation**
**55. Projectile Motion Problem:**
*On Earth, if you shoot a paper clip 96 ft/sec straight up into the air with a rubber band, the paper clip will be \( s(t) = 96t - 16t^2 \) feet above your hand at \( t \) seconds after firing.*
**A. Find \(\frac{ds}{dt}\).**
\[ \frac{ds}{dt} = 96 - 32t \]
**B. Find \(\frac{d^2 s}{dt^2}\).**
\[ \frac{d^2 s}{dt^2} = -32 \]
**C. Use the answer from part A to determine how long it takes the paper clip to reach maximum height.**
**D. When does the velocity of the particle reach \(-32\) ft/sec?**
**56. Differentiation Problem:**
*If \( f(x) = x^3 \sqrt{x^2 - 36} \), find \( f'(x) \). Simplify into one fraction.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa451162e-14ac-4cfd-a2c6-1eae7f4a5f1a%2F5d97900d-787c-4b47-bc65-0174653a360e%2Fm6yr2n_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculus Problems in Projectile Motion and Differentiation**
**55. Projectile Motion Problem:**
*On Earth, if you shoot a paper clip 96 ft/sec straight up into the air with a rubber band, the paper clip will be \( s(t) = 96t - 16t^2 \) feet above your hand at \( t \) seconds after firing.*
**A. Find \(\frac{ds}{dt}\).**
\[ \frac{ds}{dt} = 96 - 32t \]
**B. Find \(\frac{d^2 s}{dt^2}\).**
\[ \frac{d^2 s}{dt^2} = -32 \]
**C. Use the answer from part A to determine how long it takes the paper clip to reach maximum height.**
**D. When does the velocity of the particle reach \(-32\) ft/sec?**
**56. Differentiation Problem:**
*If \( f(x) = x^3 \sqrt{x^2 - 36} \), find \( f'(x) \). Simplify into one fraction.*
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 5 steps with 7 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