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S-11

S-11. A squirrel shoots his machine gun at the evil bunny family across the street. If the bullet starts from rest and exits the barrel at 1000 m/s, what is the acceleration of the bullet. Assume that the barrel is .35 m long. Vec t o r s. Unit 2. 2.1 Scalars Versus Vectors.

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S-11

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  1. S-11 A squirrel shoots his machine gun at the evil bunny family across the street. If the bullet starts from rest and exits the barrel at 1000 m/s, what is the acceleration of the bullet. Assume that the barrel is .35 m long.

  2. Vectors Unit 2

  3. 2.1 Scalars Versus Vectors

  4. SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. • b. Compare and contrast scalar and vector quantities. Standard

  5. Scalar – number with units (magnitude) Vector – has both magnitude and direction displacement velocity acceleration Vector notation – letter with arrow 2.1 Scalars Versus Vectors Compare and contrast scalar and vector quantities.

  6. 2.2 The Components of a Vector Compare and contrast scalar and vector quantities.

  7. Vectors can be broken down into components A fancy way of saying how far it goes on the x and on the y 2.2 The Components of a Vector Compare and contrast scalar and vector quantities.

  8. We calculate the sides using trig 2.2 The Components of a Vector Compare and contrast scalar and vector quantities.

  9. A represents any vector 2.2 The Components of a Vector Compare and contrast scalar and vector quantities.

  10. Then we can calculate the y 2.2 The Components of a Vector Compare and contrast scalar and vector quantities.

  11. For example if a vector that is 45 m @ 25o 2.2 The Components of a Vector Compare and contrast scalar and vector quantities.

  12. Practice Components of Vectors Compare and contrast scalar and vector quantities.

  13. If we know the components you can calculate the original the value of the vector. Magnitude is calculated using the Pythagorean theorem 2.2 The Components of a Vector Compare and contrast scalar and vector quantities.

  14. The direction is given as an angle from the +x axis Positive is counterclockwise 2.2 The Components of a Vector Compare and contrast scalar and vector quantities.

  15. Practice Resolving Vectors Compare and contrast scalar and vector quantities.

  16. 2.3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

  17. Always make a sketch of vector addition so you can approximate the correct answer Vector Addition Applet • Steps in vector addition • Sketch the vector • a. Head to tail method • b. Parallelogram method 2.3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

  18. Break vectors into their components • Add the components to calculate the components of the resultant vector • Calculate the magnitude of R • Calculate the direction of R • a. Add 180o to q if Rx is negative 2.3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

  19. 2.3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

  20. When vectors are subtracted • The vector being subtracted has its direction changed by 180o • Then we follow the steps of vector addition 2.3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

  21. Practice Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

  22. S-12 A moose is trying out his new advanced attack shuttle to hunt down defenseless baby deer. He travels north for 100 m, then goes 120 m @ 25o, and finally turns and goes 211 m @ -309o. What is his displacement?

  23. 2.4 Motion in Two Dimensions

  24. SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. • f. Measure and calculate two-dimensional motion (projectile and circular) by using component vectors. Standard

  25. Projectile Motion – object traveling through space under the influence of only gravity From the moment it is launched until the instant before it hits the ground 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

  26. Acceleration is caused by gravity In what axis? Only in the y What happens in the x? Constant velocity 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

  27. So if there is no gravity 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

  28. In the y axis, acceleration is always -9.80m/s2 All the acceleration equations apply In the y axis motion is identical to falling 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

  29. The actual pathway has constant x velocity and changing y Acceleration in the -y Projectile 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

  30. 2.5 Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component vectors.

  31. We will assume no air resistance gravity is 9.80 m/s2 the Earth is not moving (Frame of Reference) That leaves the following variables 2.5 Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component vectors.

  32. The two axis are independent of each other except for time 2.5 Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component vectors.

  33. 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  34. If an object is launched at 0o vx = vcosq = vcosq = v vy = vsinq = vsinq = 0 So our chart becomes 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  35. Now we can fill in whatever else is given in the problem 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  36. A person on a skate board with a constant speed of 1.3 m/s releases a ball from a height of 1.25 m above the ground. What variable can you fill in? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  37. A person on a skate board with a constant speed of 1.3 m/s releases a ball from a height of 1.25 m above the ground. What variable can you fill in? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  38. We are now prepared to answer some questions A) How long is the ball in the air? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  39. We are no prepared to answer some questions A) How long is the ball in the air? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  40. Basically a one dimensional problem Notice that time is the same in both the Y and the X 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  41. We can now solve for X variable if we want B) What is the x displacement? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  42. We can now solve for X variable if we want B) What is the x displacement? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  43. Practice Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  44. S-13 A pig is tied to a rocket and shot upward with an acceleration of 5 m/s2 at an angle of 35o. After 4 seconds, what is the x and y component of his velocity?

  45. 2.7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  46. All that changes if the launch angle is not zero vx = vcosq vy = vsinq 2.7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  47. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s? 2.7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  48. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s? vx = vcosq =20cos35 vx = 16.4m/s 2.7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  49. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s? vx = vcosq =20cos35 vx = 16.4m/s 2.7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

  50. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s? vy = vsinq = 20sin35 vx = 11.5 m/s 2.7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

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