Monday, February 26: Each class worked to different points of the packet, but all should have attempted the first 2 problems.
Tuesday, February 27: We completed the packet and worked the "Ross and Rachel" problem, including finding the distance between Ross and Rachel as a function of time and then finding the minimum distance between them and the time at which that happened. Here are answers to the introductory packet. Students received a second worksheet called "More Parametric Concepts" which has more equations to graph and more parameters to eliminate and more connections to make about lines, circles, ellipses and hyperbolas. Here is a PDF with some answers to the problems. However, it isn't complete.
Monday, February 5: Here are the long awaited answers to the 3rd days worksheet. And here is the ppt that I presented last year. Hopefully it will help with the projectile motion problems. You still have a quiz tomorrow.
Tuesday, February 6: JD requested answers to the Parametric Applications worksheet, so here they are:
A baseball player hits a baseball with an initial velocity of 80 mph, at an initial height of 3’ and at a 50° angle.
A)Write equations of this flight path.
x=117.3Tcos(50 degrees)
y=3+117.3Tsin(50 degrees)-16T^2
B)How far will the ball go? (I assume this is in the horizontal direction.)
425.929 ft.
C)What is the maximum height of the ball?
129.161 ft.
D)How long will the ball be in the air?
5.649 sec.
A basketball player that is about to shoot a free throw stands 3.8 meters in front of a basketball goal that is 3.5 meters above
the floor. If a 6’ player shoots the ball at a 62° angle with an initial velocity of 20 m/sec, will the basket go in?
x = 20tcos(62) y = -4.9t^2 + 20tsin(62) + 1.288 NO!!
Find a realistic shot that comes close…
Answers will vary, but think about the ball's initial velocity. Play with the numbers and then think, "Can I do this algebraically?"
Ferris Wheel Problems: Sample equations!
The assignment for tonight is to work the parametric applications worksheet and to look over the second worksheet enough to be able to ask questions about it tomorrow.
Wednesday, February 7:
Thursday, February 8: Today we looked at the algebra behind the projectile motion problems. I will post better solutions to those after I finish grading your quizzes. HOWEVER, knowing that some of you are not in class due to field trips, etc. , here is a wonderful review that covers almost anything I could find to put on your test.
Friday, February 9: Today students got back their quizzes and went over them. Then we determined if the bus from Speed could make the jump across the gap in the expressway. Here are the "Parametric Applications" problems worked. And here are better solutions (and answers) to the older Worksheet that had the baseball problem on the back. I'm still working on the answers to the wonderful review...
Monday, February 12: NOTE THE CORRECTION!! NOTE THE CORRECTION!! The 3rd days worksheet had a typo on it. Emily in 3rd period brought it to my attention and it is now fixed. To make sure you get the correct information:
To rotate parametric equations {x1, y1} counterclockwise through an angle of theta, we use the formulas:
xR = x1cos(theta) - y1sin(theta) and yR = x1sin(theta) + y1cos(theta)
Here are answers to the wonderful review. (Come back later for more.)
II. Selected Problem worked: Problem #2
III. Another problem #1
IV. Another Problem #2
Tuesday, February 27: We completed the packet and worked the "Ross and Rachel" problem, including finding the distance between Ross and Rachel as a function of time and then finding the minimum distance between them and the time at which that happened. Here are answers to the introductory packet. Students received a second worksheet called "More Parametric Concepts" which has more equations to graph and more parameters to eliminate and more connections to make about lines, circles, ellipses and hyperbolas. Here is a PDF with some answers to the problems. However, it isn't complete.
Monday, February 5: Here are the long awaited answers to the 3rd days worksheet. And here is the ppt that I presented last year. Hopefully it will help with the projectile motion problems. You still have a quiz tomorrow.
Tuesday, February 6: JD requested answers to the Parametric Applications worksheet, so here they are:
A baseball player hits a baseball with an initial velocity of 80 mph, at an initial height of 3’ and at a 50° angle.
A)Write equations of this flight path.
x=117.3Tcos(50 degrees)
y=3+117.3Tsin(50 degrees)-16T^2
B)How far will the ball go? (I assume this is in the horizontal direction.)
425.929 ft.
C)What is the maximum height of the ball?
129.161 ft.
D)How long will the ball be in the air?
5.649 sec.
A basketball player that is about to shoot a free throw stands 3.8 meters in front of a basketball goal that is 3.5 meters above
the floor. If a 6’ player shoots the ball at a 62° angle with an initial velocity of 20 m/sec, will the basket go in?
x = 20tcos(62) y = -4.9t^2 + 20tsin(62) + 1.288 NO!!
Find a realistic shot that comes close…
Answers will vary, but think about the ball's initial velocity. Play with the numbers and then think, "Can I do this algebraically?"
Ferris Wheel Problems: Sample equations!
The assignment for tonight is to work the parametric applications worksheet and to look over the second worksheet enough to be able to ask questions about it tomorrow.
Wednesday, February 7:
Thursday, February 8: Today we looked at the algebra behind the projectile motion problems. I will post better solutions to those after I finish grading your quizzes. HOWEVER, knowing that some of you are not in class due to field trips, etc. , here is a wonderful review that covers almost anything I could find to put on your test.
Friday, February 9: Today students got back their quizzes and went over them. Then we determined if the bus from Speed could make the jump across the gap in the expressway. Here are the "Parametric Applications" problems worked. And here are better solutions (and answers) to the older Worksheet that had the baseball problem on the back. I'm still working on the answers to the wonderful review...
Monday, February 12: NOTE THE CORRECTION!! NOTE THE CORRECTION!! The 3rd days worksheet had a typo on it. Emily in 3rd period brought it to my attention and it is now fixed. To make sure you get the correct information:
To rotate parametric equations {x1, y1} counterclockwise through an angle of theta, we use the formulas:
xR = x1cos(theta) - y1sin(theta) and yR = x1sin(theta) + y1cos(theta)
Here are answers to the wonderful review. (Come back later for more.)
II. Selected Problem worked: Problem #2
III. Another problem #1
IV. Another Problem #2