Projectile Motion

Chapter 3 Projectile Motion

Norjuliyati Binti Hamzah norjuliyati@uitm.edu.my

Projectile Motion Projectile Motion  An object may move in both the x and y directions simultaneously  It moves in two dimensions  The form of two dimensional motion we will deal with is an important special case called projectile motion Assumption of Projectile Motion  We may ignore air friction  We may ignore the rotation of the earth  With these assumptions, an object in projectile motion will follow a parabolic path

Projectile Motion Rules of Projectile Motion  The x-direction and y-direction of motion are completely independent of each other  The x-direction is uniform motion

ax  0  The y-direction is free fall

ay  g  The initial velocity can be broken down into its x-component and y-component

v0 x  v0 cos  0

Initial velocity for x-component

Initial velocity for y-component

v0 y  v0 sin  0

Projectile Motion Projectile Motion

Projectile Motion Projectile Motion at Various Initial Angles  Complementary values of the initial angle result in the same range  The heights will be different  The maximum range occurs at a projection angle of 45o

Projectile Motion Some Details about the Rules  x-direction

when a x  0 and v0 x  v0 cos  0 v x  v0 x  a x t

 v x  v0 x  v0 cos  0

1 2 x  v 0 x t  a x t  x  v0 x t   v0 cos  0  t 2 2 2 2 2 2 v x  v0 x  2a x x  v x  v0 x   v0 cos  0   This is the only operative equation in the x-direction since there is uniform velocity in that direction

Projectile Motion Some Details about the Rules  y-direction

when a y   g and v0 y  v0 sin  0 v y  v0 y  a y t

 v y  v0 sin  0  gt

1 1 2 2 y  v0 y t  a y t  y   v0 sin  0  t  gt 2 2 2 2 2 2 v y  v0 y  2a y y  v y   v0 sin  0   2 gy  Take the positive direction as upward  Uniformly accelerated motion, so the motion equations all hold

Projectile Motion Velocity of the Projectile  The velocity of the projectile at any point of its motion is the vector sum of its x-component and y-component at that point 2

v  vx  v y

2

and   tan

-1

vy vx

 Remember to be careful about the angle’s quadrant

Projectile Motion

Projectile Motion Summary  Provided air resistance is negligible, the horizontal component of the velocity remains constant, since

ax  0  The vertical component of the acceleration

ay  g  The acceleration in the y-direction is not zero at the top of the projectile’s trajectory  The vertical component of the velocity vy and the displacement in the y-direction are identical to those of a freely falling body  Projectile motion can be described as a superposition of two independent motions in the x-direction and y-direction