Vector and Relative motion discussion/ in class notes. Projectile Motion discussion and launch angle problem. Finish 2 d motion and review for test

Transcription

1 AP Physics 1 Unit 2: 2 Dimensional Kinematics Name: Date In Class Homework to completed that evening (before coming to next class period) 9/6 Tue (B) 9/7 Wed (C) 1D Kinematics Test Unit 2 Video 1: Vectors and Relative Motion 9/8 Thurs (B) 9/9 Fri (C) Vector and Relative motion discussion/ in class notes Unit 2 Video 2: Projectile Motion 9/12 Mon (A) LSM Projectile Motion discussion and launch angle problem 9/13 Tues (B) 9/14 Wed (C) Horizontal Launch Lab Work on Projectile Motion Problems 9/15 Thur (B) 9/16 Fri (C) Projectile Motion Packet work and Prepare for Rocket Lab 9/19 Mon (A) Rocket Lab (meet outside location TBD) 9/20 Tue (B) 9/21 Wed (C) Finish 2 d motion and review for test Study for 2D test 9/22 Thur (B) 9/23 Fri (C) 2 D test Unit Objectives: 1. An observer in a particular reference frame can describe the motion of an object using such quantities as position, displacement, distance, velocity, speed, and acceleration. a. The student is able to express the motion of an object using narrative, mathematical, and graphical representations. b. The student is able to design an experimental investigation of the motion of an object. c. The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations. 2. The acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of change of position with time. a. The student is able to make predictions about the motion of a system based on the fact that acceleration is equal to the change in velocity per unit time, and velocity is equal to the change in position per unit time. b. The student is able to create mathematical models and analyze graphical relationships for acceleration, velocity, and position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system. 1

2 AP Physics 1 Unit 2: 2 Dimensional Kinematics Name: Video 1 Link: Textbook Reference: Video 1: Vectors and Relative Motion: Read through the questions below, then watch the video, answer the following questions. Pause as needed. How are arrows used to represent vectors? Questions: How do you label arrows at angles? Show some examples on this coordinate system. What is tip to tail vector addition? Show some examples that were given in the video. How do you subtract vectors? What are the steps to solving for displacement when motion is in two dimensions? Show the steps when solving this problem: A boat moves 2.0 km east then 4.0 km north, then 3.0 km west, and finally 2.0 km south. Find resultant displacement. 2

3 AP Physics 1 Unit 2: 2 Dimensional Kinematics Name: What is a frame of reference? And how does it affect the relative motion of an object? Show how you can solve for the resultant velocity of the boat traveling across a river for this example. You are in a boat that can move in still water at 7.0 m/s. You point your boat directly East across a river to get to the other side 200 m away. The river is flowing at 4.0 m/s South. a) Determine your velocity measured by someone on the shore. To determine the time it takes to cross the 200 meter river. What equation do you use? What velocity do you use in this equation? And why? Show the solution to the time for this problem. Solve the problem for how far downstream do you land? Summarize: on the google form write a summary about what you learned from the video. Make sure to include how to add and subtract vectors, the general procedure for solving for two-dimensional displacement and what a frame of reference it is and how it effects the relative motion of an object. **Finally, be sure to write about how to determine what vector values to use when solving relative motion problems. 3

4 AP Physics 1 Unit 2: 2 Dimensional Kinematics Name: Problems to try before class (show your work below) & type you answers into the google form where indicated. 1. Given vectors P and Q, what is P + Q? 2. A factory conveyor belt rolls at 3 m/s. A mouse sees a piece of cheese directly across the belt and heads straight for the cheese at 4 m/s. What is the mouse s speed relative to the factory floor? A. 1 m/s B. 2 m/s C. 3 m/s D. 4 m/s E. 5 m/s Extra notes on vectors 4

5 AP Physics 1 Unit 2: 2 Dimensional Kinematics Name: Video 2: Textbook: Video 2: Projectile Motion Guided Notes: Questions: What is projectile motion? What are the three principles of projectile motion? In projectile motion (in the absence of air resistance), what is the acceleration: In the x-direction: In the y-direction: For an object launched horizontally, what is the initial velocity in: The x-direction? The y-direction? For an object launched at an angle what is true about: The velocity in the x-direction (in the absence of air resistance): The velocity in the y-direction? When is the velocity zero in the y-direction? What is the only equation you can use to calculate information in the x-direction? What are the equations for calculating information in the y-direction? Sketch the graphs of position and velocity for both the x and y directions below: X-direction y-direction 5

6 AP Physics 1 Unit 2: 2 Dimensional Kinematics Name: How does launch angle effect a projectiles flight? What angle produces maximum range (farthest distance)? How does air resistance effect maximum range? Solve the following horizontal projectile problem: A motor cycle speeds horizontally of a 50m high cliff. At what speed must the motor cycle leave the cliff top if it lands on the ground below 90m from the base of the cliff? Summarize: on the google form write a summary about what you learned from the video. Make sure to include the principles of projectile motion and about velocity and acceleration in the x and y direction. WSQ Questions: Answer these questions on your WSQ google form 1. A heavy red ball is released from rest 2.0 m above a flat, horizontal surface. At exactly the same instant, a yellow ball with the same mass is fired horizontally at 3.0 m/s. Which ball hits the ground first? a. The red ball hits first. b. The yellow ball hits first. c. They hit at the same time. 2. Projectiles 1 and 2 are launched over level ground with the same speed but at different angles. Which hits the ground first? Ignore air resistance. a. Projectile 1 hits first. b. Projectile 2 hits first. c. They hit at the same time. d. There s not enough information to tell. 6

7 AP Physics 1 Unit 2: 2 Dimensional Kinematics Name: additional notes: In class Launch angle problem: A football is kicked 1 m from the ground at an angle of 37º with a velocity of 20 m/s. (a) Calculate the maximum height. (b) Find the time it takes for the ball to return to the ground. (C) Calculate the total distance traveled in the x direction. (D) Calculate the velocity vector at the maximum height. (E) Determine the acceleration vector at maximum height. 7

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9 12. Three vectors are shown in the figure below. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of a) components and b) magnitude and angle with the x axis. Vector x-component y-component A B C Total 15. Your car is heading North on Route 109 with a velocity of 45.0 mph. A second car is also heading north but with a velocity of 60.0 mph. What is the velocity of the second car relative to your car? 16. You are on a railroad passenger train and you are walking toward the front of the train with a velocity of 6.00 mph relative to the passenger car in which you are riding. At the same time the train itself is moving down the tracks at 37.0 mph. What is your velocity as measured by observer at rest along the railroad tracks? 9

10 An airplane, which has an airspeed of 235 mph, heads directly West. The wind, in turn, is blowing due South with a velocity of 45.0 mph. What will be the velocity of this airplane as measured by an observer on the ground? 20. A boat, which has a speed of 12.0 m/s in still water, heads directly across a river which has a current of 7.00 m/s and is 480 meters wide (as shown in picture at right); a. What will be the velocity of this boat as measured by an observer standing along the shore? b. How long will it take for this boat to reach the opposite shore? c. How far downstream will this boat reach the opposite shore? d. What will be the final displacement of the boat when it reaches the opposite shore? 10

11 21. A boat, which has a maximum speed of 9.00 m/s, would like to reach a point on the shore directly across a river. The river has a current of 3.50 m/s and the river is 550 meters wide; a. In what direction should the boat be aimed in order for the boat to head directly across the river? b. How long will it take the boat to reach the opposite shore? 11

12 Rock thrown A is horizontally dropped from away the from top the of a cliff. cliff at The the rocks same are instant identical. that A Rock student B is using draws positive a the coordinate horizontal following system direction graphs in to is which away describe the from part positive the of the cliff, vertical and motion the of direction the origin is of rocks, up, the the coordinate system is the point the rocks were released from. What, if anything, is wrong with these graphs for the motions of the two rocks? If something is wrong, identify it and explain how to correct it. If the graphs are correct, explain why. 27. Cannonballs of different masses are shot from cannons at various angles above the horizontal. The velocity of each cannonball as it leaves the cannon is given, along with the horizontal component of that velocity, which is the same.. A ball is rolled down a ramp and launched off of a balcony. If the ball leaves the ramp with a horizontal velocity of 3.1-m/s, and the balcony is 4.3 meters tall, how far from the base of the balcony will the ball hit the ground? 12

13 28. An airplane is flying 1200 m above the ground at a speed of 200 mis. It drops a practice bomb that hits the ground after traveling a horizontal distance of 3130 m. For each of the changes below, use the choices below (i)-(v) to identify what will happen to the horizontal distance the bomb travels while falling compared to the situation above. (i) The horizontal distance will be greater than 3130 m. (ii) The horizontal distance will be less than 3130 m but not zero. (iii) The horizontal distance will be equal to 3130 m. (iv) The horizontal distance will be zero (the bomb will drop straight down). (v) We cannot determine how this change will affect the horizontal distance. For each of the following changes, only the feature(s) identified is(are) modified from the given situation above. (a) The plane's speed is tripled. Explain your reasoning. (b) The plane is climbing straight up at the release point. Explain your reasoning. (c) The plane is flying in level flight at an altitude of 1,100 m. Explain your reasoning. (d) The mass of the bomb is increased. Explain your reasoning. (e) The bomb is thrown from the plane with a vertical downward velocity of 15 mis. Explain your reasoning. 13

14 29. A baseball is thrown from point S in right field to home plate. The dashed line shows the path of the ball. Use a coordinate system with up as the positive vertical direction and to the left as the positive horizontal direction, and with the origin at home plate. Select the graph from the choices below that best represents: (i) horizontal velocity versus time graph Explain your reasoning. (ii) horizontal acceleration versus time graph Explain your reasoning (iii) vertical velocity versus time graph Explain your reasoning. (iv) vertical acceleration versus time graph Explain your reasoning. 14

15 30. A football is kicked 37 from horizontal with a velocity of 20.0m/s. Calculate a. the football s maximum height. b. the total time that the ball will be in the air. c. the distance away from the kicker that the ball will hit the ground. 31. A child stands at the edge of a cliff of height h from the ground and throws a stone at an initial speed 20 m/s downwards at an angle of 60 from the vertical as shown. The rock strikes the ground 4.0 seconds later at a distance d from the bottom of the cliff. a) Find the height, h, of the cliff. b) Find the distance, d, from the base of the cliff at which the stone lands. c) Find the vertical speed of the stone at impact. d) Find the net speed of the stone at impact. 15

16 32. A boy throws a rock horizontally off a cliff of height h with initial speed v 0. Derive equations for the following in terms of h, v 0 and fundamental constants. a. The time it takes to hit the ground. b. The distance, D, from the base of the cliff to where it lands. c. The vertical speed when it hits the ground. d. The speed of impact with the ground 16

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