Physics 101: Lecture 7, Pg 1 Lecture 7: Introduction to Physics PHY101 Chapter 2: Free Fall (2.6) è Graphical Analysis of Velocity and Acceleration (2.7) Chapter 3: è Equations of Kinematics for Constant Acceleration in 2 Dim. (3.1, 3.2) Projectile Motion (3.3)

Physics 101: Lecture 7, Pg 2 Summary of Lecture 6 l equations with constant acceleration (t 0 =0): l  x = v 0 t + 1/2 at 2 l  v = at l v 2 = v a  x l y = y 0 + v 0y t - 1/2 gt 2 l v y = v 0y - gt l v y 2 = v 0y 2 - 2g  y free fall: a y = -g = m/s 2

Physics 101: Lecture 7, Pg 3 Dennis and Carmen are standing on the edge of a cliff. Dennis throws a basketball vertically upward, and at the same time Carmen throws a basketball vertically downward with the same initial speed. You are standing below the cliff observing this strange behavior. Whose ball is moving fastest when it hits the ground? 1. Dennis' ball 2. Carmen's ball 3. Same v0v0v0v0 v0v0v0v0 Dennis Carmen H vAvAvAvA vBvBvBvB Concept Question Correct : v 2 = v g  y

Physics 101: Lecture 7, Pg 4 Free Fall - Symmetry l At a given displacement along the path of motion the magnitude of the upward velocity is equal the magnitude of the downward velocity and they point in opposite directions: v up = - v down

Physics 101: Lecture 7, Pg 5 Kinematics in Two Dimensions Constant Acceleration Consider an object which moves in the (x,y) plane from the initial position r 0, at time t 0 with velocity v 0, with constant acceleration. l position: your coordinates (just r=(x,y) in 2-D) l displacement:  r = r-r 0 change of position l velocity: rate of change of position è average :  r/  t è instantaneous: lim  t->0  r/  t l acceleration: rate of change of velocity è average:  v/  t è instantaneous: lim  t->0  v/  t Same concepts as in one dimension ! Equations of kinematics are derived for the x and y components separately. Same equations as in one dimension !

Physics 101: Lecture 7, Pg 6 Equations of Kinematics in 2 Dim. Variablex componenty component Displacement  r  x=x-x 0  y=y-y 0 Elapsed time t (t 0 =0)tt Initial velocity v 0 v 0x v 0y Final velocity vvxvx vyvy Acceleration aaxax ayay  v x = v 0x + a x t  v y = v 0y + a y t x = x 0 + t (v x +v x0 )/2y = y 0 + t (v y +v y0 )/2 x = x 0 + v 0 t + a x /2 t 2 y= y 0 + v 0 t + a y /2 t 2 v x 2 = v 0x a x  xv y 2 = v 0y a y  y

Physics 101: Lecture 7, Pg 7 Eqs. of Kinematics in 2 Dim. l The motions along the x and y directions are completely independent. They only share a common time. l Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carly (C) swims downstream. Which swimmer wins the race? A) Ann B) Beth C) Carly Time to get across = width of river / y-component of velocity A B C correct

Physics 101: Lecture 7, Pg 8 Projectile Motion A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land ? 1. Forward of the center of the car 2. At the center of the car 3. Backward of the center of the car correct

Physics 101: Lecture 7, Pg 9 Kinematics of Projectile Motion (t 0 =0) l x direction : motion with constant velocity => a x = 0 x = x 0 + v 0x t v x = v 0x l y direction : free fall => a y = - g = m/s y = y 0 + v 0y t - 1/2 g t 2 v y = v 0y – g t v y 2 = v 0y 2 – 2 g (y-y 0 )