PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 3 Announcement HW 2 due Wednesday Jan 23 3 59 am MLK Jr Day on Jan 21 Note related reading for each lecture listed on Calendar page at PHY 231 website Main points of last lecture vf vi Acceleration defined a t basic equations 1 v v0 at Equations with constant 1 2 x v0 v t Acceleration 2 1 2 3 x v0t at x v0 vf a t 2 1 4 x vf t at2 2 v2f v20 5 a x 2 2 2 a g 9 81 m s Acceleration of freefall Example 2 9a A man throws a brick upward from the top of a building Assume the coordinate system is defined with positive defined as upward At what point is the acceleration zero a A b B c C d D e None of the above B A A C C D D E Example 2 9b A man throws a brick upward from the top of a building Assume the coordinate system is defined with positive defined as upward At what point is the velocity zero a A b B c C d D e None of the above B A A C C D D E CHAPTER 3 Two Dimensional Motion and Vectors Scalars and Vectors Scalars Magnitude only Examples time distance speed Vectors Magnitude and Direction Examples displacement velocity acceleration Vectors in 2 Dimensions Vector distinguished by arrow overhead A x y y Representations x y Cartesian Polar r x Vector Addition Subtraction 2nd vector begins at end of first vector Order doesn t matter Vector addition Vector subtraction A B can be interpreted as B Order does matter A Vector Components Cartesian components are projections along the x and y axes Ax A cos Ay Asin Going backwards A Ax2 Ay2 1 Ay and tan Ax Example 3 1a The magnitude of A B is a 0 b 0 c 0 Example 3 1b The x component of A B is a 0 b 0 c 0 Example 3 1c The y component of A B 0 a 0 b 0 c 0 Example 3 2 Some hikers walk due east from the trail head for 5 miles Then the trail turns sharply to the southwest and they continue for 2 more miles until they reach a waterfalls What is the magnitude and direction of the displacement from the start of the trail to the waterfalls 3 85 miles at 21 5 degrees 5 mi 2 mi 2 dim Motion Velocity v r t It is a vector rate of change of position Trajectory Graphically Multiplying Dividing Vectors by Scalars v r t Example Vector multiplied by scalar is a vector Magnitude changes proportionately Direction is unchanged B B A B 2A A B 2 A 2 d Motion with constant acceleration X and Y motion are independent Two separate 1 d problems x vx ax y vy ay Connected by time t Important special case Projectile motion ax 0 ay g Projectile Motion v x constant X direction ax 0 x v x t v y f v y 0 gt Y direction ay g y 12 v y 0 v y f t y v y 0 t 12 gt 2 y v y f t 12 gt 2 Note we ignore air resistance rotation of earth v v g y 2 2 2 y f 2 y 0 Projectile Motion Accelerat ion is constant Pop and Drop Demo The Ballistic Cart Demo 1 Write down x t x v0 xt Finding Trajectory y x 2 Write down y t 1 2 y v0 yt gt 2 3 Invert x t to find t x t x v0 x 4 Insert t x into y t to get y x v0 y 1 g 2 y x 2 x v0 x 2 v0 x Trajectory is parabolic Example 3 3 v0 An airplane drops food to two starving hunters The plane is flying at an altitude of 100 m and with a velocity of 40 0 m s h How far ahead of the hunters should the plane release the food 181 m X Example 3 4a v0 h The Y component of v at A a b c D is 0 0 0 Example 3 4b v0 h D The Y component of v at B is a 0 b 0 c 0 Example 3 4c v0 h D The Y component of v at C is a 0 b 0 c 0 Example 3 4d v0 h D The speed is greatest at a b c d A B C Equal at all points Example 3 4e v0 h D The X component of v is greatest at a b c d A B C Equal at all points Example 3 4f v0 h D The magnitude of the acceleration is greatest at a b c d A B C Equal at all points Range Formula Good for when yf yi x vi xt 1 2 y vi yt gt 0 2 2vi y t g x 2vi xvi y g 2vi2 cos sin g vi2 x sin2 g Range Formula vi2 R sin2 g Maximum for 45 Example 3 5a A softball leaves a bat with an initial velocity of 31 33 m s What is the maximum distance one could expect the ball to travel 100 m Example 3 6 v0 h D A cannon hurls a projectile which hits a target located on a cliff D 500 m away in the horizontal direction The cannon is pointed 50 degrees above the horizontal and the muzzle velocity is 75 m s Find the height h of the cliff 68 m
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