Part 1b: Projectile Motion To analyse projectile motion, we need to make two assumptions: 1The free-fall acceleration due to gravity is constant over the range of motion 2The effect of air resistance is negligible We’ll begin by showing that the path of the projectile is parabolic. (Projectile Analysis 1)

We are interested of course in the maximum height, the time of flight and the range of the projectile. (See Projectile Analysis 2 notes).

V0tV0t -gt 2 /2 r y x Launch Point, (0,0) Range point The vector expression for the position vector r of the projectile is: r = V 0 t - gt 2 /2

“Shot Putting” In some cases, the launch point is not the same as the collision point, eg. shot put, discus, javelin, shooting, cricket, basketball etc. There are two ways of tackling this problem; one is to calculate the time of flight, the other is to use the quadratic method to solve the projectile equation. y x Launch Point, y=h B C Extra time of flight, t ex Extra range,  R  h V0V0 (See Projectile Analysis 3 notes)

Projectile down a ramp By introducing the equation for a ramp (straight line), we can find the horizontal range along the ramp for any launch angle q. By using calculus, we can also find the angle for maximum range. y x Launch Point, y=0 B C  y’ x’ V0V0  The point C has co-ordinates (x’, y’) (See Projectile Analysis 4 notes)