Projectile Motion

Notes

Projectile Motion

Definition

• Movement in 2 dimensions rather than 1

2 models

• Horizontal launch

• Kicking a stone off a bridge

• Angled launch

• Golf/base/football

• Artillery shell

• In both models, the only effect on the

projectile, after leaving the launch, is g↓

Horizontal Launch

Basic premise

• In the absence of air

resistance…

• The objects are in

free fall!

• Both objects reach

the ground at the

same time

Horizontal Launch

Analysis technique• Break the model down into vertical (y) and

horizontal (x) component columns• Vertical (y) ↓

• vo = 0 (drop model)

• g = 9.8 (always on Earth!)

• dy = height

• t = time to fall

• Horizontal (x) →

• dx = range

• vx = initial velocity in horizontal direction

• t = time to fall

vx

dy

dx

Projectile Motion

Vertical (y) Horizontal (x)

g = 9.8 dx = range

vo = 0 vx = initial velocity in x direction

dy = height t =

t =

TOOL: dy = vot + ½ g t2 (iii) TOOL: dx = vx*t

vx

dy

dx

Identify the target parameter, and start in the opposite column.

ex. If vx (horizontal column) is requested, start solving in the

vertical column

Use the time (t) value as common to both axes – the time taken to

follow the parabolic path is the same as a simple drop!

Ex. Horizontal

A baseball rolls off a 0.7 m high desk and

strikes the floor 0.25 m away from the base

of the desk.

How fast was it rolling?

vx

dy

dx

Solution

1) vertical

• dy = vot + ½ g t2

• 0.7 = 0 + ½ (9.8) t2

• t = 0.38 seconds (use in the “other” column)

2) horizontal

• dx = vx*t

• 0.25 = vx* 0.38

• vx = 0.66 m/s

vx

dy

dx

Practice

Your turn!

What if the projectile is launched

at an angle to the horizontal?

Angled Launch Projectile Motion

Definition

• The motion of the projectile is uniquely

defined by:

• Its launch angle (Ө) and

• its initial velocity (vo)

Angled Launch Parameters

Angled Launch

Angled Launch – refer to sheet

Max Height:

• dymax = (V0 sin )2/2g

Range:

• d xmax= V02 sin (2 ) / g

Time to max height:

• t = (V0 sin )/g

Total time in air (hang time)

• (time up=time down)

• ttotal = 2 (V0 sin )/g

Comparing Trajectories

Max range angle

Which angle provides the maximum down range (x) distance?

Practice time

Your turn!