Activity 1.1.2. The following questions concern the position function given by s(t) = 64-16(t − 1)², considered in Preview Activity 1.1.1. a. Compute the average velocity of the ball on each of the following time intervals: [0.4, 0.8], [0.7, 0.8]. [0.79, 0.8], [0.799, 0.8], [0.8, 1.2], [0.8, 0.9], [0.8, 0.81]. [0.8, 0.801]. Include units for each value. b. On the graph provided in Figure 1.1.1, sketch the line that passes through the points A = (0.4, s(0.4)) and B = (0.8, 8(0.8)). What is the meaning of the slope of this line? In light of this meaning, what is a geometric way to interpret each of the values computed in the preceding question? c. Use a graphing utility to plot the graph of s(t) = 64-16(t - 1)² on an interval containing the value t = 0.8. Then, zoom in repeatedly on the point (0.8, s(0.8)). What do you observe about how the graph appears as you view it more and more closely? d. What do you conjecture is the velocity of the ball at the instant t = 0.8? Why? 64 feet A 56 48 B S sec 0.4 0.8 1.2
Activity 1.1.2. The following questions concern the position function given by s(t) = 64-16(t − 1)², considered in Preview Activity 1.1.1. a. Compute the average velocity of the ball on each of the following time intervals: [0.4, 0.8], [0.7, 0.8]. [0.79, 0.8], [0.799, 0.8], [0.8, 1.2], [0.8, 0.9], [0.8, 0.81]. [0.8, 0.801]. Include units for each value. b. On the graph provided in Figure 1.1.1, sketch the line that passes through the points A = (0.4, s(0.4)) and B = (0.8, 8(0.8)). What is the meaning of the slope of this line? In light of this meaning, what is a geometric way to interpret each of the values computed in the preceding question? c. Use a graphing utility to plot the graph of s(t) = 64-16(t - 1)² on an interval containing the value t = 0.8. Then, zoom in repeatedly on the point (0.8, s(0.8)). What do you observe about how the graph appears as you view it more and more closely? d. What do you conjecture is the velocity of the ball at the instant t = 0.8? Why? 64 feet A 56 48 B S sec 0.4 0.8 1.2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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not use ai please
![Activity 1.1.2. The following questions concern the position function given
by s(t) = 64-16(t − 1)², considered in Preview Activity 1.1.1.
a. Compute the average velocity of the ball on each of the following time
intervals: [0.4, 0.8], [0.7, 0.8]. [0.79, 0.8], [0.799, 0.8], [0.8, 1.2], [0.8, 0.9],
[0.8, 0.81]. [0.8, 0.801]. Include units for each value.
b. On the graph provided in Figure 1.1.1, sketch the line that passes
through the points A = (0.4, s(0.4)) and B = (0.8, 8(0.8)). What is the
meaning of the slope of this line? In light of this meaning, what is a
geometric way to interpret each of the values computed in the preceding
question?
c. Use a graphing utility to plot the graph of s(t) = 64-16(t - 1)² on an
interval containing the value t = 0.8. Then, zoom in repeatedly on the
point (0.8, s(0.8)). What do you observe about how the graph appears as
you view it more and more closely?
d. What do you conjecture is the velocity of the ball at the instant t = 0.8?
Why?
64
feet
A
56
48
B
S
sec
0.4
0.8
1.2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57e2977b-57d0-4fda-b158-b847f2c4cd7a%2Fd7df72a8-85d2-4c61-b650-486db9542c8e%2Fk6n8vj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Activity 1.1.2. The following questions concern the position function given
by s(t) = 64-16(t − 1)², considered in Preview Activity 1.1.1.
a. Compute the average velocity of the ball on each of the following time
intervals: [0.4, 0.8], [0.7, 0.8]. [0.79, 0.8], [0.799, 0.8], [0.8, 1.2], [0.8, 0.9],
[0.8, 0.81]. [0.8, 0.801]. Include units for each value.
b. On the graph provided in Figure 1.1.1, sketch the line that passes
through the points A = (0.4, s(0.4)) and B = (0.8, 8(0.8)). What is the
meaning of the slope of this line? In light of this meaning, what is a
geometric way to interpret each of the values computed in the preceding
question?
c. Use a graphing utility to plot the graph of s(t) = 64-16(t - 1)² on an
interval containing the value t = 0.8. Then, zoom in repeatedly on the
point (0.8, s(0.8)). What do you observe about how the graph appears as
you view it more and more closely?
d. What do you conjecture is the velocity of the ball at the instant t = 0.8?
Why?
64
feet
A
56
48
B
S
sec
0.4
0.8
1.2
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