3-2: Kinematics in 2 D

75 m/s 50 m/s Rank the scenarios by how long each cannonball will be in the air (longest to shortest). V0 = 0m/s H=100m H=100m H=100m A B C Prediction 1

The vertical motion of all 3 tennis balls was identical! In the vertical direction, the tennis balls are accelerating (the position vs. time graph is a parabola) The slope of the v vs. t graph shows that the acceleration in the y-direction is -9.8m/s/s – the acceleration due to gravity! Vertical Motion

The only factor that affects how long the tennis ball is in the air is the height from which it falls. The time was the same for all three scenarios (with minor variations due to experimental error) Vertical Motion

75 m/s 50 m/s Rank the scenarios by how far each cannonball will travel horizontally (furthest to shortest). V0 = 0m/s H=100m H=100m H=100m A B C Prediction 1

In the horizontal direction, the tennis balls are moving with constant velocity (see v vs. t graph) There is NO acceleration in the horizontal direction. Horizontal Motion

The only factor that affects the distance each tennis ball travels horizontally is the speed with which it is released. Horizontal Motion

The x part of the motion (horizontal) occurs exactly as it would if the y (vertical) part did not occur. The y part of the motion occurs exactly as it would if the x part did not occur. 2-D Kinematics

2-D Kinematics The x and y motions are independent of each other! This allows us to treat 2-D motion as two distinct 1-D problems – one for the x direction, one for the y-direction. 2-D Kinematics

2-D Kinematics X- direction Variable Y-Direction x Displacement y ax Acceleration ay vx Final Velocity vy v0x Init Velocity v0y t Time 2-D Kinematics

2-D Kinematics X direction Y direction vx=v0x+axt vy=v0y+ayt x=1/2(v0x+vx)t y=1/2(v0y+vy)t x=x0+v0xt+1/2axt2 y=y0+v0yt+1/2ayt2 vx2=v0x2+2aΔx vy2=v0y2+2aΔy 2-D Kinematics

EX 1: An object is launched at an angle of 25° with a speed of 80 mph EX 1: An object is launched at an angle of 25° with a speed of 80 mph. What are the horizontal and vertical components of velocity? < 72.5, 33.8 > mph 80 mph 80sin25° 25° 2-D Kinematics 80cos25°

EX 2: You are standing on the roof of a shed, and shoot a paintball at your buddy below you. The paintball leaves your gun at an angle of -50° and a speed of 300 feet per second (204.5 mph or 329 km/h). What are the horizontal and vertical components of velocity? < 192.8, -36.98 > ft/s vx=300cos(-50) 50° vy=300sin(-50) 300ft/s 2-D Kinematics

EX 3: An object is launched at an angle of 38° with a speed of 57 m/s EX 3: An object is launched at an angle of 38° with a speed of 57 m/s. What are the horizontal and vertical components of ACCELERATION? < 0, -9.8 > m/s2 a = 9.8 m/s2 a = 9.8 m/s2 v0= 57 m/s a = 9.8 m/s2 38° 2-D Kinematics

Stop & Think S&T 4.3 Knight p 102: A 50 g marble rolls off a table and lands 2 m from the base of the table. A 100 g marble rolls off the same table with the same speed. It lands at distance: a) Less than 1 m b) 1 m c) Between 1 and 2 m d) 2 m e) Between 2 and 4 m f) 4 m 2-D Kinematics

An airplane moving horizontally with a constant velocity of +115m/s at an altitude of 1050m. The directions to the right and upward have been chosen as positive directions. The plane releases a care package that falls to the ground along a curved trajectory. Determine the time required for the package to hit the ground. 2-D Kinematics

Where will the package hit the ground? (relative to the release point) What is the magnitude and direction (angle) of the final velocity vector that the package has just before it hits the ground? 2-D Kinematics

Assignment 3B: P 82 #12, 14 – 17 2-D Kinematics