Physics 101: Lecture 27, Pg 1 Two Dimensional Dynamics Physics 101: Lecture 06 l Today’s lecture will cover Textbook Chapter 4

Physics 101: Lecture 27, Pg 2 ACT – from lecture 5 l The speed of an object in free fall (Neglect Air Resistance) A. Always increases. B. is constant. C. Always decreases. D. May increase or decrease or be constant. E. May increase or decrease but is never constant. 16 t v t s=|v|

Physics 101: Lecture 27, Pg 3 Brief Review Thus Far Newton’s Laws of motion:  F=ma Kinematics: Dynamics Today we work in 2 Dimensions! 05 x = x 0 + v 0 t + ½ a t 2 v = v 0 + a t v 2 = v a (x-x 0 )

Physics 101: Lecture 27, Pg 4 2-Dimensions l X and Y are INDEPENDENT! l Break 2-D problem into two 1-D problems y x 7

Physics 101: Lecture 27, Pg 5 Position, Velocity and Acceleration l Position, Velocity and Acceleration are Vectors! l x and y directions are INDEPENDENT! 10

Physics 101: Lecture 27, Pg 6 Velocity in Two Dimensions 5 m/s 3 m/s A ball is rolling on a horizontal surface at 5 m/s. It then rolls up a ramp at a 25 degree angle. After 0.5 seconds, the ball has slowed to 3 m/s. What is the magnitude of the change in velocity? A) 0 m/s B) 2 m/s C) 2.6 m/s D) 3 m/s E) 5 m/s y x 15 25°

Physics 101: Lecture 27, Pg 7 Acceleration in Two Dimensions 5 m/s 3 m/s A ball is rolling on a horizontal surface at 5 m/s. It then rolls up a ramp at a 25 degree angle. After 0.5 seconds, the ball has slowed to 3 m/s. What is the average acceleration? y x 18

Physics 101: Lecture 27, Pg 8 Kinematics in Two Dimensions l x = x 0 + v 0x t + 1/2 a x t 2 l v x = v 0x + a x t l v x 2 = v 0x 2 + 2a x  x l y = y 0 + v 0y t + 1/2 a y t 2 l v y = v 0y + a y t l v y 2 = v 0y 2 + 2a y  y x and y motions are independent! They share a common time t 21

Physics 101: Lecture 27, Pg 9 Train Demo Act 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? A. Forward of the center of the car B. At the center of the car C. Backward of the center of the car 25

Physics 101: Lecture 27, Pg 10 ACT A flatbed railroad car is accelerating down a track due to gravity. The ball is shot perpendicular to the track. Where will it land? A. Forward of the center of the car B. At the center of the car C. Backward of the center of the car 31 y x

Physics 101: Lecture 27, Pg 11 Projectile Motion ACT One marble is given an initial horizontal velocity, the other simply dropped. Which marble hits the ground first? A) dropped B) pushed C) They both hit the ground at the same time 35

Physics 101: Lecture 27, Pg 12 You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting? 1 Right at the monkey 2 Below the monkey 3 Above the monkey Monkey Pre-Flight Demo - monkey 39

Physics 101: Lecture 27, Pg 13 x = x 0 x = x 0 yg y = - 1 / 2 g t 2 See text: 4-3 x = v 0 t x = v 0 t yg y = - 1 / 2 g t 2 Shooting the Monkey... 40

Physics 101: Lecture 27, Pg 14 Shooting the Monkey... yvg y = v 0y t - 1 / 2 g t 2 l Still works even if you shoot upwards! yg y = y / 2 g t 2 Dart hits the monkey! 41

Physics 101: Lecture 27, Pg 15 Projectile Motion a x = 0 a y = -g  x = x 0 + v 0x t  v x = v 0x  y = y 0 + v 0y t - ½ gt 2  v y = v 0y – g t  v y 2 = v 0y 2 – 2 g  y Choose direction where you “know” information Solve kinematics in that direction. Use t from that direction as t in other direction 43

Physics 101: Lecture 27, Pg 16 Throw ball to Monkey You throw a ball to a monkey who is on a platform 12 meters above and 5 meters to the right of you. Determine the speed and angle you should throw it such that it “just reaches” the monkey. 5 m 12 m 48

Physics 101: Lecture 27, Pg 17 Summary of Concepts l X and Y directions are Independent! è Position, velocity and acceleration are vectors è “Share” l F = m a applies in both x and y direction l Projective Motion è a x = 0 in horizontal direction è a y = g in vertical direction 50