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# UConn PHYS 1501Q - Projectile Motion

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Phys 1501Q 1st Edition Lecture 5Outline of Last Lecture: Vector ManipulationsI. Vectorsa. Example Displacement VectorII. ScalarsIII. Vector Addition VisuallyIV. Vector Subtraction VisuallyV. Vector Multiplication Visually (Scalar)VI. Vector on a Coordinate SystemVII. Vector LengthVIII. Unit VectorsIX. Writing Vector in Terms of Unit ComponentsX. Vector Addition Using ComponentsXI. Example Vector Addition Calculation of CoordinatesXII. Vector Multiplication Overviewa. Scalarb. Dot ProductCross ProductOutline of Current Lecture: Projectile MotionThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.I. Projectile MotionII. Effect of Gravity on Projectile MotionIII. Example: Shooting a Monkey in a TreeIV. Path Followed By ProjectileV. Horizontal Motion = constantVI. Vertical Motion = changingVII. Relating Horizontal to Vertical MotionsHorizontal Range EquationVIII. Horizontal Range CalculationIX. Angle That Optimizes RangeX. Baseball Horizontal Range ExampleCurrent Lecture: Projectile Motion I. Projectile MotionAn object moving in two dimensions under the influence of gravityII. Effect of Gravity on Projectile Motion- Gravity affects vertical motiono It is constant, downward, acceleration- Gravity does NOT affect horizontal motion/acceleration- THUS: We can treat vertical and horizontal motion INDEPENDENTLY from each otherIII. Example: Shooting a Monkey in a TreeYou fire a gun at t=0, aimed horizontal to and at the same height as the monkey in the tree. As soon as the gun is fired (at t=0) the monkey lets go of the tree and falls. - The bullets always hit the monkey!! Why?We are dropping both objects at t=0. (ignore air resistance). Thus the objects are always at the same height, at the same time when they are falling. Horizontal speed does NOT matter. ** This is also true if the gun were fired at an angle upward at the monkey!IV. Path Followed By Projectile- Vox = magnitude of velocity*cosΘVox = Vo*cosΘ- Voy = magnitude of velocity * sinΘVoy = Vo*sinΘV. Horizontal Motion = constant- Horizontal motion stays the same- Ax = 0 (acceleration = 0)- Velocity always equals initial velocity (Vi)-X −X0=V0 x∗t =V0cosθVI. Vertical Motion = changing- Vertical motion changes due to the constant acceleration of gravity- Ay – g-Y −Y0=V0 y∗t −12¿2=V0sinθt−12¿2VII. Relating Horizontal to Vertical Motions/Horizontal Range Equation- Eliminate t- Take Xo and Yo to be zero1.xV0cosθ=t (sub this expression in where t would go in the vertical motion equation)2.y=V0sinθ(xV0cosθ)−12g(xV0cosθ)23. EQUATION = V2(¿¿ 0 cosθ)2∗x2(tanθ)x−g¿VIII. Horizontal Range Calculation- You have an initial velocity Vo and angle Θ. Calculate the horizontal range that it goes.- Ball hits ground at y = 0 (there are two times y=0, when motion first begins and when it hits the ground at the end)-Range=V02gsinθIX. Angle That Optimizes Range- We know: max value of sin2Θ = 1o This occurs when 2Θ = 90° or when Θ=45°- Whenever you want to maximize distance Θ always =45°X. Baseball Horizontal Range ExampleHow far will a ball go if hit at 30° at 100 mph?1. Convert mph into ft/sVo = 100 mi * 5280f * 1hr = 147f 1 hr 1 mi 3600 sec sec2. Plug into range formula3.Range=V02gsinθ=147232sin ⁡(60)4. Range = 585 f5. Note: 32 f/s^2 is equal to 9.8m/s^2 for

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