e. At what time will the ball be on the way back down and 720 feet above the ground? f. Make a table of values and record the average velocity in the intervals the moments before the ball hits the ground. (Note: Suppose your answer to number 1 is b. Then 1 second before hitting water means the time interval is [b-1, b]. Time Interval Time Frame 1 second before hitting ground ½ second before hitting ground 0.1 second before hitting ground 0.01 seconds before hitting ground 0.001 seconds before hitting ground Average Velocity g. Approximately how fast was the ball moving the instant it hit the ground?
e. At what time will the ball be on the way back down and 720 feet above the ground? f. Make a table of values and record the average velocity in the intervals the moments before the ball hits the ground. (Note: Suppose your answer to number 1 is b. Then 1 second before hitting water means the time interval is [b-1, b]. Time Interval Time Frame 1 second before hitting ground ½ second before hitting ground 0.1 second before hitting ground 0.01 seconds before hitting ground 0.001 seconds before hitting ground Average Velocity g. Approximately how fast was the ball moving the instant it hit the ground?
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
DO Problems E, F, G, ony
![**Problem 9**
a. A ball is thrown straight up with an initial velocity of 224 ft/sec, so its height (in feet) is given by
\[ h(t) = 224t - 16t^2. \]
b. Find the average velocity of the ball over the interval \([4, 4.1]\).
c. When will the ball hit the ground?
d. Find the inverse function that gives the time \( t \) at which the ball is at height \( h \) as the ball travels downward.
e. At what time will the ball be on the way back down and 720 feet above the ground?
f. Make a table of values and record the average velocity in the intervals the moments before the ball hits the ground. (Note: Suppose your answer to number 1 is \( b \). Then 1 second before hitting the ground means the time interval is \([b - 1, b]\).)
| Time Frame | Time Interval | Average Velocity |
|---------------------------------|---------------|------------------|
| 1 second before hitting ground | | |
| ½ second before hitting ground | | |
| 0.1 second before hitting ground| | |
| 0.01 seconds before hitting ground | | |
| 0.001 seconds before hitting ground | | |
g. Approximately how fast was the ball moving the instant it hit the ground?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e38577e-9620-4c07-818f-a04b4c1cdbce%2F072ad4ac-bb74-4103-a17f-a55590c5dcbf%2Fv4n4oc_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 9**
a. A ball is thrown straight up with an initial velocity of 224 ft/sec, so its height (in feet) is given by
\[ h(t) = 224t - 16t^2. \]
b. Find the average velocity of the ball over the interval \([4, 4.1]\).
c. When will the ball hit the ground?
d. Find the inverse function that gives the time \( t \) at which the ball is at height \( h \) as the ball travels downward.
e. At what time will the ball be on the way back down and 720 feet above the ground?
f. Make a table of values and record the average velocity in the intervals the moments before the ball hits the ground. (Note: Suppose your answer to number 1 is \( b \). Then 1 second before hitting the ground means the time interval is \([b - 1, b]\).)
| Time Frame | Time Interval | Average Velocity |
|---------------------------------|---------------|------------------|
| 1 second before hitting ground | | |
| ½ second before hitting ground | | |
| 0.1 second before hitting ground| | |
| 0.01 seconds before hitting ground | | |
| 0.001 seconds before hitting ground | | |
g. Approximately how fast was the ball moving the instant it hit the ground?
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