PHYS 1443 – Section 003 Lecture #6AnnouncementsKinetic Quantities in 1d and 2dProjectile MotionSlide 5Projectile MotionExample of Projectile MotionHorizontal Range and Max HeightSlide 9Maximum Range and HeightExample for a Projectile MotionExample cont’dObservations in Different Reference FramesRelative Velocity and AccelerationForceMore ForceNewton’s First Law and Inertial FramesMonday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu1PHYS 1443 – Section 003Lecture #6•Motion in Two Dimensions–Projectile Motion•Reference Frames•Forces•Newton’s Laws of MotionMonday, Sept. 15, 2003Dr. Jaehoon YuMonday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu2Announcements•Quiz #2 this Wednesday, Sept. 17•e-mail distribution list:29 of you have subscribed so far. –There will be negative extra credit from this week•-1 point if not done by 5pm, Friday, Sept. 12•-3 points if not done by 5pm, Friday, Sept. 19•-5 points if not done by 5pm, Friday, Sept. 26–A test message will be sent Wednesday for verification purpose•Remember the 1st term exam, Monday, Sept. 29, two weeks from today–Covers up to chapter 6.–No make-up exams•Miss an exam without pre-approval or a good reason: Your grade is an F.–Mixture of multiple choice and essay problemsMonday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu3Kinetic Quantities in 1d and 2dInst. Acc.Average Acc.Inst. VelocityAverage VelocityDisplacement2 Dimension1 DimensionQuantitiesifxxx ifrrr ififxttxxtxvififttrrtrvdtrdtrvt 0limdtdxtxvtx 0limififttvvtvaifxixfxxttvvtva220limdtrddtvdtvat220limdtxddtdvtvaxxtxWhat is the difference between 1D and 2D quantities?Monday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu4Projectile Motion•A 2-dim motion of an object under the gravitational acceleration with the assumptions–Free fall acceleration, -g, is constant over the range of the motion–Air resistance and other effects are negligible•A motion under constant acceleration!!!! Superposition of two motions–Horizontal motion with constant velocity ( no acceleration )–Vertical motion under constant acceleration ( g )Monday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu5aiifvxtcosShow that a projectile motion is a parabola!!!cosixivv fx 2221sin 21gttvtgtvyiiyif2cos21cossiniifiifiifvxgvxvyPlug t into the aboveIn a projectile motion, the only acceleration is gravitational one whose direction is always toward the center of the earth (downward).ax=0What kind of parabola is this?222cos2tanfiiiffxvgxyiiyivvsinx-component y-component jaiayxjgtvtviixicosMonday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu6Projectile Motion The only acceleration in this motion. It is a constant!!Monday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu7Example of Projectile MotionA ball is thrown with an initial velocity vv=(20ii+40jj)m/s. Estimate the time of flight and the distance the ball is from the original position when landed.Which component determines the flight time and the distance? mtgtyf0 2140 mtvxxif160820 Flight time is determined by y component, because the ball stops moving when it is on the ground after the flight.Distance is determined by x component in 2-dim, because the ball is at y=0 position when it completed it’s flight.sec880or 0 gtt 080 gttMonday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu8Horizontal Range and Max Height•Based on what we have learned in the previous pages, one can analyze a projectile motion in more detail–Maximum height an object can reach–Maximum rangetavvyyiyfAt the maximum height the object’s vertical motion stops to turn around!!vviihgvtiAsinWhat happens at the maximum height?0sin AigtvMonday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu9Horizontal Range and Max Height 221tgtvhyyifSince no acceleration in x, it still flies even if vy=0 AxitvR 2gvRii2sin22sin21sinsingvggvviiiiiigvyiif2sin22gvviiiisincos2Monday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu10Maximum Range and Height•What are the conditions that give maximum height and range of a projectile motion?gvhii2sin22This formula tells us that the maximum height can be achieved when i=90o!!!gvRii2sin2This formula tells us that the maximum range can be achieved when 2i=90o, i.e., i=45o!!!Monday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu11Example for a Projectile Motion•A stone was thrown upward from the top of a cliff at an angle of 37o to horizontal with initial speed of 65.0m/s. If the height of the cliff is 125.0m, how long is it before the stone hits the ground? smvvixi/9.5137cos0.65cos o2210.125 gttvyyif02502.7880.92502.7822 tttgt 80.92)250(80.942.782.782tstst 4.10or 43.2 st 4.10smvviiyi/1.3937sin0.65sin oSince negative time does not exist.Monday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu12Example cont’d•What is the speed of the stone just before it hits the ground? gtvvyiyf smvvvyfxf/5.818.629.512222xixfvv•What are the maximum height and the maximum range of the stone? Do these yourselves at home for fun!!!smgtvii/8.624.1080.91.39sin smvi/9.5137cos0.65cos oMonday, Sept. 15, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu13Observations in Different Reference FramesResults of Physical measurements in different reference frames could be differentObservations of the same motion in a stationary frame would be different than the ones made in the frame moving together with the moving object.Consider that you are driving a car. To you, the objects in the car do not move while to the person outside the car they are moving in the same speed and direction as
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