Part 1b: Projectile Motion

To analyse projectile motion, we need to make two assumptions:

1 The free-fall acceleration due to gravityis constant over the range of motion

2 The 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 themaximum height, the time of flightand the range of the projectile.

(See Projectile Analysis 2 notes).

V0t-gt2/2

r

y

x

Launch Point, (0,0)

Range point

The vector expression for the position vector r of the projectile is:

r = V0t - gt2/2

“Shot Putting”

In some cases, the launch point is not thesame as the collision point, eg. shot put, discus,javelin, shooting, cricket, basketball etc. There are two ways of tackling this problem; one is tocalculate the time of flight, the other is to use thequadratic method to solve the projectile equation.

y

x

LaunchPoint, y=h

B

C

Extra time of flight, tex

Extra range, R

h

V0

(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 forany launch angle q. By using calculus, we can also findthe angle for maximum range.

y

x

LaunchPoint, y=0

B

C

y’

x’

V0

The point C hasco-ordinates (x’, y’)

(See Projectile Analysis 4 notes)