PHYS 100: Lecture 4 PROJECTILE MOTION. y = (v 0 /v T ) x (g/2v T2 )x 2. Velocity of Train v T. Physics 100 Lecture 4, Slide y(m)

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1 PHYS : Lecture 4 PROJECTILE MOTION.4. Velocity of Train T y(m) x(m) y ( / T ) x (/ T )x Physics Lecture 4, Slide

2 Music Who is the Artist? A) Miles Dais B) Wynton Marsalis C) Chris Botti D) Nina Simone E) Chet Baker West Coast cool jazz from the 5 s In honor of Valentine s Day next week: His definitie ersion of My Funny Valentine Hypnotizin oice. DVD Must-See: Twiliht of his career/life Van Morrison does Send in the Clowns Physics Lecture 4, Slide

3 POINTS POINTS POINTS UNDERSTANDING is the GOAL; POINTS are what we ie to et you to do the work PERFORMANCE QUIZ EXAM (MIDTERM) FINAL Phys Fall Data EFFORT DISC HW LECT (PL,CP,LECT) What are the takeaway messaes from this raph? A and B students are indistinuishable on EFFORT (>95% a) C and D students do not put in the same effort (7-8%) A and B students are distinuished by QUIZ and EXAM rades C and D students do poorly on exams (esp quizzes) NOTE: Performance on Quizzes is your best indicator of your CURRENT understandin Physics Lecture 4, Slide 3

4 Interactie Examples How To Do Homeworks REPEAT OF SLIDE FROM LEC These problems help you deelop a concept-based problem solin approach If you can t calculate the answer to the problem, select the Help Button You et another question to help you deelop your Plan! Eentually, we ie away the store : This is an Example!!! Physics Lecture 4, Slide 4

5 THE BIG IDEAS NOTE: THE BIG IDEAS ARE ALWAYS GIVEN IN THE LAST SLIDE. Motion described as -D freefall in one frame is described as projectile motion in all other frames.. Description of projectile motion is superposition of x and y motions a) Constant elocity in x (horizontal) b) Constant acceleration in y (ertical) Physics Lecture 4, Slide 5

6 THE PLAN FOR TODAY. The Plan is to build to an understandin of the Battleship CheckPoint. How will we do this? a) We will do clicker questions whose explanations will feature equations b) The purpose is not to memorize these equations but to see how you can REASON with equations!!! Physics Lecture 4, Slide 6

7 Ball on a Cart DEMO: Ball is ejected straiht up from a cup in a cart moin at constant elocity. When it falls back, will it land (A) in back of the cup (B) in the cup (C) in front of the cup A B C This is THE POINT: Descriptions of same motion from two different reference frames Cart frame: motion is -D free fall: ball oes up, stops, and comes straiht back down y x t y t t x y C Ground frame: motion is -D projectile: ball follows parabolic trajectory y x t y t t x t y G x C x G Physics Lecture 4, Slide 7

8 Ball on a Cart II DEMO: Ball is ejected straiht up from a cup in a cart moin at constant acceleration. When it falls back, will it land (A) in back of the cup (B) in the cup (C) in front of the cup A B C a WHAT S THE DIFFERENCE? Ground frame: motion OF BALL is -D projectile: parabolic trajectory motion OF BALL in x-direction is motion at constant elocity motion OF CART in x-direction is motion with increasin elocity x BALL t x CART t + at Physics Lecture 4, Slide 8

9 CheckPoint Without air resistance, an object dropped from a plane flyin at constant speed in a straiht line will: (A) Quickly la behind the plane (C) Moe ahead of the plane (B) Remain ertically under the plane (D) It depends on the object You said: quickly la behind the plane because after it has been dropped it no loner has the same elocity as the plane and it is oin in a different direction also Same as Ball on Cart!! This is just like the boat moin at a constant speed and someone from the boat throwin it straiht up and the ball would fall straiht down. So the object dropped from a plane flyin will fall straiht down, which is ertically under the plane A B C D Physics Lecture 4, Slide 9

10 Practice (with a Point) Two objects are thrown straiht up from the same heiht. Object is ien an initial elocity while Object is ien an initial elocity. Which object is in the air the lonest? (A) Object (B) Object (C) Same amount of time t t How do we calculate how lon the ball stays in the air? At the top (/ of the time in the air) the elocity of the ball is zero The elocity is bein reduced by m/sec eery second t Physics Lecture 4, Slide

11 More Practice Two objects are thrown with the same initial elocity from the same heiht. Object is thrown at anle θ 45 o while Object is thrown at anle θ 6 o Which object is in the air the lonest? (A) Object (B) Object (C) Same amount of time sin 45 ( ) y sin 45 t 45 o 6 o sin 6 ( ) y sin 6 t How do we calculate how lon the ball stays in the air? At the top (/ of the time in the air) the y-component of the elocity of the ball is zero The y-component of the elocity is bein reduced by m/sec eery second sin6 o sin45 o y t Physics Lecture 4, Slide

12 More Practice Two objects are thrown with different initial elocities from the same heiht. Object is thrown with at anle θ 6 o while Object is thrown with.5 at anle θ 3 o Which object is in the air the lonest? (A) Object (B) Object (C) Same amount of time sin 6 ( ) y sin 6 t.5 6 o 3 o.5 sin 3 ( ) y.5 sin 3 t How do we calculate how lon the ball stays in the air? At the top (/ of the time in the air) the y-component of the elocity of the ball is zero The y-component of the elocity is bein reduced by m/sec eery second Sin6 o 3/ o sin6 o.5 sin3 o y t Sin3 o /.5.5 Sin3 o 3/4.75 Physics Lecture 4, Slide

13 The Point What determines how lon an object will stay in the air when thrown? (A) Only the manitude of the initial elocity (B) Only the horizontal component of the initial elocity (C) Only the ertical component of the initial elocity (D) Both the horizontal & ertical component of the initial elocity How do we calculate how lon the ball stays in the air? At the top (/ of the time in the air) the y-component of the elocity of the ball is zero The y-component of the elocity is bein reduced by m/sec eery second y sinθ t sinθ Physics Lecture 4, Slide 3

14 CheckPoint A man and his son are standin at the ede of the cliff. They both pick up ery similar rocks and throw them horizontally off of the cliff. The man s rock traels twice as far from the base of the cliff as the rock the boy threw. If they both threw their rocks at the same time and from the same heiht, which one hit the round first? (A) The boy s rock (C) They land at the same time (B) The man s rock (D) Need more information You said: The boys rock would hit first because it did not o as far. The mans rock went farther and so it will take loner to hit the round. The y component (which is raity) is the same, therefore, since their initial position on the y-axis is identical, their fall will happen at the same place and ultimately result in the rocks landin simultaneously DEMO A B C D Physics Lecture 4, Slide 4

15 How Hih? Two objects are thrown with different initial elocities from the same heiht. Object is thrown with at anle θ 6 o while Object is thrown with.5 at anle θ 3 o Which object oes the hihest? (A) Object (B) Object (C) Same amount of time sin 6 ( ) y sin 6 t.5 6 o 3 o.5 sin 3 ( ) y.5 sin 3 t How do we calculate how hih the ball oes? At the top (/ of the time in the air) the y-component of the elocity of the ball is zero Find the time when this occurs (we e done that a lot today) Determine the heiht at this time. THE MATH: y sin θt t t sinθ y max sinθ sinθ sinθ y max sin Physics Lecture 4, Slide 5 θ

16 CheckPoint 3 A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship ets hit first? (A) A (B) At the same time You said: (C) B (D) more info The trajectory of the missile is different for each shot but the actual distance that each missile traels is the same. This means that the missile will be traelin the same distance with the same elocity makin the time of each missiles fliht the same. It hits B first because no matter how fast the shells are traelin raity pulls the sames for both and so the one that does not hae to trael as hih will hit its taret first. In order to answer this, I need to know the anle of the trajectories and the distance each ship is away from the battleship A B C D Physics Lecture 4, Slide 6

17 CheckPoint 3 A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship ets hit first? (A) A (B) At the same time (C) B (D) more info We certainly hae not been ien the elocities and the distances Howeer, is there somethin about this picture that tells us enouh to be able to answer the question???? YOU BETCHA!!! The shell to A oes hiher which means its initial ertical component of the elocity is reater than that of the shell that went to B. We can use this fact to compare the time in the air of the shells. Physics Lecture 4, Slide 7

18 CheckPoint 3 A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship ets hit first? (A) A (B) At the same time (C) B (D) more info WHAT HAVE WE LEARNED ABOUT PROJECTILE MOTION TODAY?? sinθ The time in the air is determined by the ertical component of the initial elocity y max sin θ The maximum heiht is determined by the ertical component of the initial elocity A oes HIGHER so A takes loner!! Physics Lecture 4, Slide 8