Unit Kinematics Module Investigating Motion in Two Dimensions page 1 of 2 A First Look at Projectile Motion The vector forms of the master equations of kinematics for constant acceleration can be used to describe free fall in two dimensions To solve a projectile motion problem you need to know the initial position and velocity of the object Two objects simultaneously dropped to the ground will land at the same instant even if one has horizontal velocity Projectile motion is free fall in two dimensions Examples of objects experiencing projectile motion are a rocket after its engines stop a high jumper making a jump a baseball thrown through the air and the dart shot out of a toy gun You already know that objects in free fall accelerate m downward at 9 8 2 The master equations of s kinematics with constant acceleration can be used to describe projectile motion Because objects in free fall accelerate only in the vertical direction the horizontal component of acceleration is zero The terms containing ax drop out of the x components of projectile motion An important consequence is that the horizontal velocity is constant in projectile motion The value of ay in the y component forms of the m equations of kinematics is 9 8 2 when the s coordinate system points in the downward direction m and 9 8 2 when the coordinate system points in s the upward direction www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1816 rev 06 26 2001 Unit Kinematics Module Investigating Motion in Two Dimensions page 2 of 2 A First Look at Projectile Motion Two balls are ejected simultaneously from a platform above the ground One ball falls directly to the ground The other ball has an initial velocity in the x direction The balls land at the same instant Motion in the x direction is independent from motion in the y direction Because both balls have identical initial position velocity and constant acceleration in the y direction their vertical paths are identical The horizontal component of both balls velocity remains constant throughout the fall in one case it is zero in the other case it is vix Thelma and Louise drive their car off a 500 m cliff at m 50 You can calculate how long it takes them to s reach the ground using the y components of the second equation of kinematics Choose a coordinate system where the ground is at 0 m and up is in the positive direction The value of yi is 500 m m m v iy is 0 and ay is 9 8 2 You can solve for s s t to find that it takes about 10 s for the car to land www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1816 rev 06 26 2001
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