PHYSICS 220 Lecture 06 Projectile Motion Textbook Sections

PHYSICS 220 Lecture 06 Projectile Motion Textbook Sections 4. 2 Lecture 6 Purdue University, Physics 220 1

2 -Dimensions • X and Y are INDEPENDENT! y x • Break 2 -D problem into two 1 -D problems Lecture 6 Purdue University, Physics 220 2

Relative Velocity • We often assume that our reference frame is attached to the Earth. What happen when the reference frame is moving at a constant velocity with respect to the Earth? • The motion can be explained by including the relative velocity of the reference frame in the description of the motion. The ground velocity of an Example airplane is the vector sum of the air velocity and the wind velocity. Using the air as the intermediate reference frame, ground speed is: V(PG)=V(PA) +V(AG) Lecture 6 Purdue University, Physics 220 3

i. Clicker You are on a train traveling 40 mph North. If you walk 5 mph sideways across the car (W), what is your speed relative to the ground? A) >40 mph B) 40 mph C) <40 mph N + 5 mph W = 41 mph NW 5 40 Lecture 6 Purdue University, Physics 220 4

Exercise 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 correct y x t = d / vy Ann vy = v cos( ) A B C Beth vy = v Carly vy = v cos( ) Lecture 6 Purdue University, Physics 220 5

Exercise What angle should Ann take to get directly to the other side if she can swim 5 mph relative to the water, and the river is flowing at 3 mph? VAnn, ground = Vann, water+Vwater, ground y x x-direction: sin( ) = |Vwater, ground|/ |Vann, water| A B C sin( ) = 3/5 Lecture 6 Purdue University, Physics 220 6

Velocity in Two Dimensions 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 y has slowed to 3 m/s. What is the magnitude of the change in velocity? x x-direction y-direction vix = 5 m/s vfx = 3 m/s cos(25) viy = 0 m/s vfy = 3 m/s sin(25) vx = 3 cos(25)– 5 =-2. 28 m/s vy = 3 sin(25)=+1. 27 m/s 3 m/s 5 m/s Lecture 6 Purdue University, Physics 220 7

Acceleration in Two Dimensions 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 y has slowed to 3 m/s. What is the average acceleration? x-direction x y-direction 3 m/s 5 m/s Lecture 6 Purdue University, Physics 220 8

Kinematics in Two Dimensions x = x 0 + v 0 xt + 1/2 axt 2 y = y 0 + v 0 yt + 1/2 ayt 2 vx = v 0 x + axt vy = v 0 y + ayt vx 2 = v 0 x 2 + 2 ax x vy 2 = v 0 y 2 + 2 ay y x and y motions are independent! They share a common time t Lecture 6 Purdue University, Physics 220 9

Projectile Motion x-direction: ax = 0 x = x 0 + v 0 x t vx = v 0 x y-direction: ay = -g y = y 0 + v 0 y t - ½ gt 2 vy = v 0 y – g t vy 2 = v 0 y 2 – 2 g y Lecture 6 Purdue University, Physics 220 10

Velocity of a Projectile Velocity components of a projectile Lecture 6 Purdue University, Physics 220 11

Independence of the Vertical and Horizontal motion of Projectiles Lecture 6 Purdue University, Physics 220 12

The Range of a Kickoff A place-kicker kicks a football at an angle of =400 above the horizontal axis. The initial speed of the ball is v 0=22 m/s. Ignore air resistance and find the range R that the ball attains. v 0=22 m/s H =400 R Lecture 6 Purdue University, Physics 220 13

The Range of a Kickoff • Use the equations x = x 0 + v 0 xt vx = v 0 x y = y 0 + v 0 yt - 1/2 gt 2 vy = v 0 y - gt vy 2 = v 0 y 2 - 2 g y • The range is a characteristic of the horizontal motion • You need v 0 x and v 0 y but you have been given v 0 x = v 0 cos = (22 m/s)cos 400 = 17 m/s Lecture 6 v 0 y Purdue University, Physics 220 v 0 x 14

The Range of a Kickoff • We could be done if we know the time of flight of the kickoff • The time of flight can be determined from y equations. For example the time to get to height H is v v 0 y 0 v 0 x v 0 y =v 0 sin = (22 m/s)sin 400=14 m/s • Therefore the time to determine the range is 2. 9 s • The range depends on the angle at which the football is kicked. Maximum range is reached for =450 Lecture 6 Purdue University, Physics 220 15

Range of a Projectile Lecture 6 Purdue University, Physics 220 16

i. Clicker A ball is thrown into the air and follows a parabolic trajectory. At the highest point in the trajectory, A) The velocity is zero, but the acceleration is not zero. B) Both the velocity and acceleration are zero. C) The acceleration is zero, but the velocity is not zero. D) Neither the acceleration nor the velocity is zero. Lecture 6 Purdue University, Physics 220 17

Shooting the Monkey 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. On the other hand, you also know that the dart will not travel in a straight line, but rather in a parabolic path like any other projectile. In order to hit the monkey with the dart, where should you point the gun before shooting? A) Right at the monkey B) Below the monkey C) Above the monkey Lecture 6 Purdue University, Physics 220 18

Shooting the Monkey y = y 0 - 1 / 2 g t 2 y = v 0 y t - 1/2 g t 2 Dart hits the monkey! Lecture 6 Purdue University, Physics 220 19