Motion in Two Dimensions Reading Notes

Transcription

1 Motion in Two Dimensions Reading Notes Name: Section 3-1: Vectors and Scalars What typeface do we use to indicate a vector? Test Your Understanding: Circle the quantities that are vectors. Acceleration Atomic Number Density Displacement Distance Energy Force Mass Money Position Speed Temperature Time Velocity Volume Section 3-2: Addition of Vectors Graphical Methods In the statement D R = D 1 + D 2, what is the vector D R called? When two vectors are, we just use addition to find the resultant. When two vectors are, we just use subtraction to find the resultant. When two vectors are, we use the Pythagorean Theorem to find the resultant. What does the statement D R D 1 + D 2 mean? When does the equal to part apply to that statement? Test Your Understanding: In the three examples below, a set of vectors is shown on the top grid. Using the tail-to-tip method, show how to add those vectors in the bottom grid, and then draw the resultant.

2 Section 3-3: Subtraction of Vectors, and Multiplication by a Scalar Test Your Understanding: The vectors A and B are shown below. Show the resultant of each of the operations indicated. A B B A 2B ½B ½B Section 3-4: Adding Vectors by Components Explain what the components of a vector are. What do the components tell you? Write the equations that give the components V x and V y of a vector V in terms of the vector s magnitude V and its direction.

3 The direction of a vector,, is always measured relative to what axis/direction? Which rotation direction is considered a positive direction? Write the equations that give the magnitude V and direction of a vector V in terms of its components V x and V y. Example: The vector V shown starts with components (40, 30) at time t = 0. Each second, the vertical component decreases by 10. Answer the following: When is V the shortest? What is V s shortest length? When is V again the same length that it was at time t = 0? Is vector V ever zero? Explain: Section 3-5: Projectile Motion In Figure 3-17 on page 58, at what times is the ball considered a projectile? When an object is a projectile, what is the shape of the path that it travels? What is Figure 3-19 on page 59 trying to convey? Look at Figure 3-18 and Figure 3-20 on pages 58 and 59. Explain the following in words: How is the direction of velocity related to the parabolic path at each point? (Starts with a T.) What happens to the horizontal component of velocity as the projectile travels? What happens to the vertical component of the velocity as the projectile travels? At what point in the path is the vertical component of the velocity zero?

4 At what point in the path is the speed of the projectile zero? A person throws a ball in such a way that its speed is zero at one particular point in its path. How did the person throw the ball? When an object travels as a projectile, what type of motion occurs in the horizontal direction? When an object travels as a projectile, what type of motion occurs in the vertical direction? Test Your Understanding: A projectile travels from point A to point G as shown below. Find the components of the velocity vector at point A. Then determine the components of velocity at every other point; use the fact that each point occurs 1 second after the previous point. Also use g = 10 m/s 2. Section 3-6: Solving Problems Involving Projectile Motion Write the equation for horizontal position as a function of time for projectile motion: Write the equation for vertical position as a function of time for projectile motion: Write the equation for vertical velocity as a function of time for projectile motion: Identify all the symbols that you used above: x = v 0x = y 0 = g = y = v 0y = v y = t =

5 Example 1: A student throws a ball horizontally off of the roof of the Chase Bank Building, 125 m above the ground. The ball strikes the ground 100 m away from the base of the building. How fast did the student throw the ball? (Use g = 10 m/s 2.) Draw a Diagram Here! Solution: Sketch a graph of each of the following as a function of time: Important Points To Remember About Horizontal Launch: The horizontal initial velocity is equal to. The vertical initial velocity is equal to. The projectile motion equations simplify to and. Example 2: A student on the 0-m line of a metric football field kicks a football at an angle of 53 with an initial velocity of 25 m/s. Using g = 10 m/s 2, find: Draw a Diagram Here!

6 (a) the time the football is in the air (b) how far the football lands from the student (c) the highest height the football reaches Sketch a graph of each of the following as a function of time: Important Points To Remember About Ground-To-Ground Launch: The final velocity is equal to. Use this to find the time by.

7 Example 3: It is November 22, 1963 in an alternate universe. The motorcade transporting President Kennedy is traveling down Main Street when Kennedy spots Oswald in a much taller Book Depository window. Kennedy immediately draws a crossbow and, at time t = 0, fires an arrow directly at Oswald. The air does not affect the arrow in any way. Oswald tries to dodge the arrow by jumping out the window from rest at exactly time t = 0. What are the components of the arrow s initial velocity? At what time does the arrow reach the plane of the building? At what height above the launch point does the arrow reach the building? At what height above the launch point is Oswald when the arrow reaches the building? Section 3-8: Relative Velocity Example: A boat starts from House O on a river that is 200 m wide. House A is 200 meters downstream (in the direction the river flows) and on the same side of the river as O. House B is 200 meters upstream (in the opposite direction the river flows) and on the same side of the river as O. House C is directly across the river from O. A boat leaving House O can travel 5 m/s if the river is still. However, today the river has a current speed of 3 m/s as shown in the diagrams.

8 If the boat goes to House A, how much time will that trip take? If the boat goes to House B, how much time will that trip take?

9 If the boat points directly across the river to House C, will the boat reach House C? Why or why not? What must the boat do to reach House C without being swept downstream? If the boat does go directly toward House C, how long will that trip take?