Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the...
-
Upload
angela-reed -
Category
Documents
-
view
217 -
download
0
Transcript of Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the...
![Page 1: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/1.jpg)
Gravity, Technology, Quadratic Like Equations
![Page 2: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/2.jpg)
• An object near the surface of earth is under the influence of gravity
• We can model this by using a quadratic equation
![Page 3: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/3.jpg)
Properties
• Exclude air resistance and mechanical forces– Simpler version
• Only applicable for short distances– IE, not launching a rocket into space or satellite in
a low orbit
• h = • g = force due to gravity; t = time (seconds), ho
002
2
1htvgt
![Page 4: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/4.jpg)
Equation
• h = • g = force due to gravity• t = time (seconds) • ho = initial height
• V0 = initial velocity
002
2
1htvgt
![Page 5: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/5.jpg)
• Example. You stand at the top tier of seats in a stadium, and decide to throw a ball down to ground level. The ball starts with an upward velocity of 90ft/s, and is 65 feet above ground at the moment you throw the ball. When does the ball hit land?
![Page 6: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/6.jpg)
Using your Calculator
• For the previous problem, we can use our calculator to help us plot or graph the motion represented by the model
• Look further into solutions and behavior
![Page 7: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/7.jpg)
• Example. Using the previous problems, locate the roots of the quadratic. What is the shape of the quadratic?
![Page 8: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/8.jpg)
Quadratic-Like Equations
• Some equations can be written in a form similar to quadratics
• Solve just like we do with quadratics– Factor– Zero Product Property
![Page 9: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/9.jpg)
• Quadratic-Like = an equation which can be written as aA2 + bA + c = 0.
• Look for the actual variable A first (or, what part that will represent A)
![Page 10: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/10.jpg)
• Ex. Solve the quadratic (x2 + 2x)2 – 7(x2 + 2x) – 8 = 0
• What phrase can represent A?
![Page 11: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/11.jpg)
• Ex. Solve the quadratic like equation (x2 – 6x)2 + 4(x2 – 6x) – 5 = 0
![Page 12: Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.](https://reader035.fdocuments.us/reader035/viewer/2022072113/5697c0301a28abf838cdb03b/html5/thumbnails/12.jpg)
• Assignment• Pg. 94• 46-53, 57-67 odd