Motion in Two

Dimensions

6

6.1 Introduction

ESCCW

In Grade 10, we studied motion in one dimension and briefly lookedat vertical mo-

tion. In this chapter wewill discuss vertical motion and also look at motion in two

dimensions. In Grade 11, we studied the conservation of momentum and looked at

applications in one dimension. In this chapterwe will look at momentum in two di-

mensions.

See introductory video:VPnio at http://www.everythingscience.co.za

6.2 Vertical Projectile Motion ESCCX

In Grade 10, we studied the motion of objectsin free fall and we sawthat an object

in free fall falls with gravitational acceleration g. Now we can considerthe motion of

objects that are thrownupwards and then fall back to the Earth. We call this projectile

motion and we will only consider the situation where the object is thrownstraight

upwards and then fallsstraight downwards - this means that there is no horizontal

displacement of the object, only a vertical displacement.

Motion in a Gravitational Field ESCCY

When an object is in the earth’s gravitational field, it always accelerates downwards,

towards the centre of the earth, with a constantacceleration g, no matter whether the

object is moving upwards or downwards. This isshown in Figure 6.1.

Tip

Projectiles moving up-

wards or downwards in

the earth’s gravitational

field always accelerate

downwards with a

constant acceleration

g. Note: acceleration

means that the veloc-

ity changes; it either

becomes greater or

smaller.

This means that if an object is moving upwards, its velocity decreasesuntil it stops

(vf= 0 m·s−^1 ). This is the maximum height that the object reaches, because after this,

the object starts to fall.

Tip

Projectiles have zero ve-

locity at their greatest

height.

Consider an object thrown upwards from a vertical height ho. We have seen that the

object will travel upwards with decreasing velocity until it stops, at whichpoint it starts

falling. The time that ittakes for the object to fall down to height hois the same as the

time taken for the object to reach its maximumheight from height ho.