Motion under gravity

A particle which is moving under gravity alone is moving in a straight line under constant acceleration, so all the concepts applied to linear motion under constant acceleration may equally be applied here.
On the ordinary level paper the acceleration due to gravity is taken as 10 m/s2, whereas on the higher level the value for g is 9.8 m/s2.
We adopt the same sign convention here as in Cartesian geometry, namely "up" is positive, "down" is negative.
The equations of motion are now:


 
 
 
 
 
 

There are a number of points worth noting:
1. Stick to the sign convention
2. Take the point of projection as the point where s = 0
    This means that if the particle goes below the point of projection its s value is negative
3. At its highest point the velocity of the particle is zero
4. The time the particle is in the air may be determined by using 
    If the particle lands at the same level at which it was projected then  s = 0
    If, however, it lands h metres below its point of projection then,  s = -h
5. If a particle is dropped from another, as the other moves, then the initial velocity of the particle is that of the one from which it was dropped.

An example to illustrate these points.

1992 Leaving Certificate Higher Level.
A baloon ascends vertically at a uniform speed.
7.2 s after it leaves the ground a particle is let fall from the balloon.
The particle takes 9 s to reach the ground.
Calculate the height from which the particle was dropped.

 

 Particle:

 
 

 Baloon:


Equate h's: