If a rock is dropped from a height of 219 feet, the rock's position t seconds after it is dropped is given by the function s(t) = -16t² + 219. Answer the following. Your answers must be exact. How long does it take the rock to hit the ground? 219 4 seconds Find the average velocity of the rock from the time it is dropped to the time it hits the ground. x feet per second -32
If a rock is dropped from a height of 219 feet, the rock's position t seconds after it is dropped is given by the function s(t) = -16t² + 219. Answer the following. Your answers must be exact. How long does it take the rock to hit the ground? 219 4 seconds Find the average velocity of the rock from the time it is dropped to the time it hits the ground. x feet per second -32
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...
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![### Problem Description:
If a rock is dropped from a height of 219 feet, the rock's position \( t \) seconds after it is dropped is given by the function \( s(t) = -16t^2 + 219 \). Answer the following. Your answers must be exact.
1. **How long does it take the rock to hit the ground?**
\[ \frac{\sqrt{219}}{4} \] seconds
2. **Find the average velocity of the rock from the time it is dropped to the time it hits the ground.**
\[ -32 \] feet per second
3. **Apply the Mean Value Theorem to determine the time that the rock's instantaneous velocity will be equal to its average velocity.**
\[ -1 \] seconds after the rock is thrown](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdc195bb-9009-47db-866e-65b6514806e8%2F5ab57014-d14e-476d-b132-ab42e8175f4f%2Fore2fmq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Description:
If a rock is dropped from a height of 219 feet, the rock's position \( t \) seconds after it is dropped is given by the function \( s(t) = -16t^2 + 219 \). Answer the following. Your answers must be exact.
1. **How long does it take the rock to hit the ground?**
\[ \frac{\sqrt{219}}{4} \] seconds
2. **Find the average velocity of the rock from the time it is dropped to the time it hits the ground.**
\[ -32 \] feet per second
3. **Apply the Mean Value Theorem to determine the time that the rock's instantaneous velocity will be equal to its average velocity.**
\[ -1 \] seconds after the rock is thrown
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