SPH3U1 Lesson 12 Kinematics PROJECTILE MOTION LEARNING GOALS Students will: Describe the motion of an object thrown at arbitrary angles through the air. Describe the horizontal and vertical motions of a projectile. Solve projectile motion problems. PATH OF A PROJECTILE 1. Logon to a computer. Go to the website http://www.walter-fendt.de/ph14e/projectile.htm Change the initial height to 0. Run the simulation. a) What is the shape of the path followed by the projectile? b) Try different angles of inclination. Which one gives you the maximum distance? c) What other angle gives you the same distance as 30 0? As 55 0? d) What is the rule for finding two angles that give the same distance? VELOCITY OF A PROJECTILE 2. Click on the button to show velocity. Also click on the box for Slow Motion. Run the simulation. You will see the overall velocity vector as well its horizontal and vertical components. a) Focus on the horizontal component only. Run the simulation. What does it show for the horizontal velocity? Why do you think this is happening? b) Focus on the vertical velocity component. Run the simulation. Describe what is happening to the vertical velocity component. What is causing this? c) Focus on the overall velocity. Does it ever become zero? Why or why not? d) Look at how the overall velocity is oriented to the path of the projectile. What word do we use to describe this relationship? 1
SPH3U1 Lesson 12 Kinematics e) If you increase the initial velocity, describe what happens to the distance travelled: height reached: ACCELERATION OF A PROJECTILE 3. Click on the acceleration button. Run the simulation. a) What can you say about the acceleration of the projectile? What causes it to be like this? b) Why is there no horizontal component to the acceleration? SOLVING PROJECTILE MOTION PROBLEMS IMPORTANT RULE: The horizontal part of the motion is independent from the vertical motion. The two parts can be solved separately. HOWEVER, the TIME to complete the horizontal motion is the same as the TIME to complete the vertical motion. CONCEPT PROBLEMS 5. A student pushes a coin off the edge of a counter with some horizontal velocity. At the instant the coin goes over the edge, a second student drops a second coin from countertop level so it falls vertically to the floor. Which coin hits the floor first? Explain your answer. Think about the IMPORTANT RULE above. TRY IT. 6. A similar experiment to the one above is done. A rifle is fired horizontally over a large flat plane. At the instant the rifle is fired, a student drops a second identical bullet from the same height as the rifle. Which bullet hits the ground first? Explain. 7. A monkey is hanging from a tree branch. A scientist wants to shoot the monkey with a tranquilizer dart so she can study the monkey. She knows the monkey will be startled by the sound of the tranquilizer gun and will let go of the branch at the instant the gun is fired. Where should the scientist aim to hit the monkey? (Above it, below it or directly at it?) Explain. To check this answer, go to youtube.com and search for MIT Physics Monkey and Gun. Go to full screen mode. Pause the video just before the projectile is launched. Use the side of a piece of paper placed along the edge of the gun to see where it is aimed. Remove the paper and continue watching the video. Fix your answer above if necessary. 2
SPH3U1 Lesson 12 Kinematics EXAMPLE A ball is rolled at 2.2 m/s along a counter top that is 1.2 m above the floor. It rolls over the edge of the counter top. a) How far horizontally does it travel before hitting the floor? b) What is the velocity of the ball when it hits the floor? SPLIT THE GIVENS INTO HORIZONTAL AND VERTICAL QUANTITIES Quantity Horizontal (x) Vertical (y) let up be + initial velocity 2.2 m/s 0 final velocity 2.2 m/s acceleration 0-9.8 m/s 2 displacement -1.2 m time Horizontal: The acceleration is 0 so the velocity is constant. Vertical: The acceleration is the acceleration due to gravity. The negative sign means down. The displacement is also down as the ball starts vertically at the counter height and ends vertically on the floor which is lower. Time: is the same for both x and y. a) Now you can solve the problem as normal. You have enough information to solve for the remaining vertical quantities. Solve for time: Vertical: = + 1.2 =0+ 9.8 =0.495 Horizontal: solve for distance since v is constant = = 2.2 0.495 =1.09 b) The final velocity has two components. We already know the final horizontal velocity (2.2 m/s). Now find the final vertical velocity. Vertical: = + Combining: =0+ 9.8 0.495 = 4.85 = 2.2 +4.85 =5.33 / =.. =66 therefore the velocity of the ball on contact with the floor is 5.3 m/s [66 0 below horizontal]. 2.2 m/s θ 4.85 m/s HOMEWORK Do P78 Q1-2, P81 Q1-2 (Top) Q2-8 (Bottom) 3
SPH3U1 Lesson 13 Kinematics PROJECTILE MOTION II LEARNING GOALS Students will describe the motion of an object thrown at arbitrary angles through the air Students will describe the horizontal and vertical motions of a projectile Students will solve projectile motion problems PATH OF A PROJECTILE Logon to a computer. Go to the website http://www.walter-fendt.de/ph14e/projectile.htm All the examples you did in the previous lesson had either the initial horizontal or the initial vertical velocity equal to zero. Or, the two were separately specified. Click on Slow motion and on the velocity button. Run the simulation. The thickest, darkest velocity vector is the overall velocity. You will now solve a problem where this is the only initial velocity you are given. EXAMPLE 1. A golfer hits a golf ball with an initial velocity of 54 m/s [42 0 above the horizontal]. The ball lands on an elevated green that is 14 m higher that the level from which the golfer hit the ball. a) How far away horizontally from the golfer does the ball land? b) What is the velocity of the ball when it lands? You will solve this example using what you already know with some guidance. Fill in the quantities you know in the table. For the initial vertical and horizontal velocities, take the velocity given above and determine its components using trigonometry. Quantity Horizontal (x) Vertical (y) let up be + initial velocity final velocity acceleration 0-9.8 m/s 2 displacement time 1
SPH3U1 Lesson 13 Kinematics a) Now solve the vertical problem to determine the time. This will produce a quadratic equation that will give you two answers. If you do it right, you will get the times 0.4 s and 7.0 s. Which of the two times is the one you want to use? Why? Now determine the horizontal distance the ball travels. You should get 279 m. b) Find the final vertical velocity (32 m/s [down]). Add it to the final horizontal velocity (40 m/s) to get the final answer (51 m/s [39 0 below the horizontal]). HOMEWORK Do p 92 #2-4 p113 #27, 29, 30, 32, 33 2
SPH3U Physics Kinematics Projectile Problem Solving As we learned yesterday when an object moves freely under the influence of gravity it accelerates in the downward direction only. The horizontal components of the velocity remain constant. Motion in the horizontal direction can be described by Motion in the vertical direction can be described by the 5 equations of motion. Solve the following question in your groups using the whiteboards: An arrow is shot from a height of 20.0m with an initial horizontal velocity of 18.0 m/s. a. Sketch (Must be checked by teacher before moving on) b. How far in the horizontal direction will the arrow fall?
SPH3U Physics Kinematics Ramp & Cup Projectile Test Group Members: Purpose: To analyze the motion of a horizontally launched projectile. Setup: Data (from teacher): Height of lab bench: Average horizontal displacement of fall: Calculations: 1. Determine the time the ball takes to fall. 2. Determine the projectile s horizontal velocity. The Test: To test the power of predictability your teacher will tape a cup to a retort stand at a certain height above the ground. Using your results above you must calculate where the retort stand must be placed on the floor so the marble lands in the cup (ie. Find the horizontal displacement between edge of table and middle of cup). Complete a full formal solution. Once you have done the calculation bring it to your teacher to test your prediction. Height of cup for your group (obtain from teacher): Based on your calculations, where should the cup be placed? To be completed by teacher: The marble landed in near far from the cup