Next week, we will look at some applications of Local Extrema, but we will do a simple example here that doesn't require much setup. Solve each part, providing explanations wherever necessary. Suppose you throw launch a ball into the air, and its height is given by the function h (t) = −4.9t² +60t + 5 where h is in meters and t is seconds after you launch the ball. Do the following: A. Find the velocity of the ball at time t B. At some point the ball is going to start falling back down. What is the velocity of the ball at the moment it stops going up and starts going down? Hint: you should not do any math to answer this part of the question; think about what you would actually see the ball do at this moment. C. Using your answer to parts A and B, find the time t that the ball starts falling D. Find the height of the ball when it starts falling E. Graph h, and describe how what you see relates to your answers to parts A-D F. Now, consider the following prompt: "Find the maximum height of the ball." What we did for parts A-D is actually how we would answer this question. Compare your process for this discussion post to what we learned in section 4.3.
Next week, we will look at some applications of Local Extrema, but we will do a simple example here that doesn't require much setup. Solve each part, providing explanations wherever necessary. Suppose you throw launch a ball into the air, and its height is given by the function h (t) = −4.9t² +60t + 5 where h is in meters and t is seconds after you launch the ball. Do the following: A. Find the velocity of the ball at time t B. At some point the ball is going to start falling back down. What is the velocity of the ball at the moment it stops going up and starts going down? Hint: you should not do any math to answer this part of the question; think about what you would actually see the ball do at this moment. C. Using your answer to parts A and B, find the time t that the ball starts falling D. Find the height of the ball when it starts falling E. Graph h, and describe how what you see relates to your answers to parts A-D F. Now, consider the following prompt: "Find the maximum height of the ball." What we did for parts A-D is actually how we would answer this question. Compare your process for this discussion post to what we learned in section 4.3.
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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Question
Transcribed Image Text:Next week, we will look at some applications of Local
Extrema, but we will do a simple example here that
doesn't require much setup. Solve each part, providing
explanations wherever necessary.
Suppose you throw launch a ball into the air, and its
height is given by the function
h (t) = −4.9t² + 60t +5
where h is in meters and t is seconds after you launch the
ball. Do the following:
A. Find the velocity of the ball at time t
B. At some point the ball is going to start falling back down.
What is the velocity of the ball at the moment it stops
going up and starts going down? Hint: you should not do
any math to answer this part of the question; think about
what you would actually see the ball do at this moment.
C. Using your answer to parts A and B, find the time t
that the ball starts falling
D. Find the height of the ball when it starts falling
E. Graph h, and describe how what you see relates to your
answers to parts A-D
F. Now, consider the following prompt: "Find the maximum
height of the ball." What we did for parts A-D is actually
how we would answer this question. Compare your
process for this discussion post to what we learned in
section 4.3.
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