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Physics 218 Lecture 6 Dr. David Toback Chapter 4, continued Kinematics in Two Dimensions Today Problems Projectile Motion The physics of the universe: The horizontal and vertical Equations of Motion behave independently This is why we use vectors in the first place Projectile Motion

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## Physics 218 Lecture 6

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**Physics 218Lecture 6**Dr. David Toback Physics 218, Lecture VI**Chapter 4, continued**Kinematics in Two Dimensions TodayProblems Physics 218, Lecture VI**Projectile Motion**The physics of the universe: The horizontal and vertical Equations of Motion behave independently This is why we use vectors in the first place Physics 218, Lecture VI**Projectile Motion**• This is the heart and culmination of what we have learned so far • You can rest assured there will be a problem like one in lecture today on the exam Physics 218, Lecture VI**How to use the Tricks and Methods**• Next we’ll do an example problem like one of the homework problems in the text book • Solve this problem using the right method • Draw a diagram • Convert the numbers to variables • Solve to get a formula • Plug in the numbers at the end • Check • Reasonable numbers? • Silly numbers? • Another way to do the same problem? Physics 218, Lecture VI**How to Solve Problems**The trick for all these problems is to break them up into the X and Y directions Physics 218, Lecture VI**Firing up in the air at an angle**A ball is fired up in the air with speed Vo and angle Qo. Ignore air friction. The acceleration due to gravity is g pointing down. What is the final velocity here? Physics 218, Lecture VI**Important Definition ;-)**Word: Defenestration Definition: The act of throwing someone or something out of a window Physics 218, Lecture VI**Push BEVO out of a window**Reveille pushes BEVO directly out of a window that is a height h above the ground. Two Aggies observe that BEVO hits the ground a distance D from the base of the building. Assuming BEVO was moving horizontally at the top (and ignoring air friction), how fast must Reveille have pushed her? h y=0 D Physics 218, Lecture VI**Kick a football**A football is kicked at angle Q with respect to the ground with speed V0. Calculate: • The maximum height • The velocity at the maximum height • The time of travel before the football hits the ground • How far away it hits the ground • What angle maximizes the distance traveled Assume the ball leaves the foot at ground level and ignore air resistance Physics 218, Lecture VI**Winner: Not my job award**Physics 218, Lecture VI**More Realistic Punt**h A football is kicked at angle Q0 with a speed V0. The ball leaves the punters foot h meters above the ground. How far does it travel, in the X direction, before it hits the ground? Physics 218, Lecture VI**Rescue Plane**You are the pilot of a rescue plane and you are flying a plane with a horizontal speed of Vp. Your mission is to drop supplies for some mountain climbers on a ridge a vertical distance h below. To do this you have to release the supplies a horizontal distance R in advance of the mountain climbers. What vertical velocity should you give the supplies so that they arrive precisely at the the climbers position? Physics 218, Lecture VI**Next Week**New Material: Not on the 1st exam • Chapter 5:Read for Next time • Newton’s Laws of Motion • HW2 due Monday • Cover CH. 3&4 in recitation, due the following Monday • Lab 3 (posted on the website) Physics 218, Lecture VI**End of Lecture Notes**Physics 218, Lecture VI**Next time…**• Reading: None, you’ve already finished Chapter 3 & 4 already • Homework: • HW1 was due yesterday • HW2 covered in recitation this week; due this coming Monday • Start working on HW for Chap 3 & 4 • Next time: More on kinematics in two dimensions Physics 218, Lecture VI**Ball Dropping**Analyze Vertical and Horizontal separately!!! • Ay = g (downwards) • Ax = 0 • Constant for Both cases!!! Vx = 0 Vx>0 Physics 218, Lecture VI**A weird consequence**Prove that an object projected horizontally will reach the ground at the same time as an object dropped vertically Physics 218, Lecture VI**Firing up in the air at an angle**A ball is fired up in the air with velocity Vo and angle Qo. Ignore air friction. The acceleration due to gravity is g pointing down. What is the final velocity here? Physics 218, Lecture VI**Rescue Plane**You are the pilot of a rescue plane. Your mission is to drop supplies to isolated mountain climbers on a rocky ridge a height h below. If your plane is traveling horizontally with a speed of VO: • How far in advance of the recipients (horizontal distance) must the goods be dropped? Physics 218, Lecture VI**Rescue Plane cont.**• Suppose instead, that your plane can’t get to that position. Instead you must release the supplies a horizontal distance D in advance of the mountain climbers. What vertical velocity should you give the supplies so that they arrive precisely at the the climbers position. • What is the speed of the supplies as they hit the ground? Physics 218, Lecture VI**Announcements: Exam 1**• We will move the date of Exam 1 from Tuesday Feb 11th. • Next week you need to do the reading for Chapter 4, Chapter 3-9 and Chapter 5. There will be quizzes on both. • Note: You will get recitation on Chapter 3 and turn in your Homework before the exam. Physics 218, Lecture VI**Next Week**• Chapter 4: (NOT ON 1st EXAM) • Dynamics • Newton’s Laws of Motion • Finish HW3. Labs & Rec/Web as usual • Exam Thursday: Here during regular time • Bring a calculator and ruler • Formula sheet will be provided (on the web already) • Will cover: • Chapter 1 (1-6) • Calculus 1 • Chapter 2 (1-7) • Chapter 3 (1-8, 10) Physics 218, Lecture VI**Example: 3-8**Derive a formula for the horizontal range, R, of a projectile in terms of its initial velocity (v0 & Q) before the projectile travels before returning to its original height Physics 218, Lecture VI

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