5.06 Summary acceleration due to gravity and projectile motion
For a free body close to the Earth's surface which is only acted on by gravity;

The Earth's gravity will cause it to accelerate at 9.81 ms ^{2}

we can use suvat equations to solve problems involving acceleration due to gravity but we usually modify the symbols to highlight vertical
motion and acceleration due to gravity

For objects that have initial upward velocity before changing direction and falling back to the ground we use

y = ut  ^{1}/_{2}gt^{2}

v = u  gt

The minus sign accounts for the fact that g acts downward

For objects dropped from rest from above the Earth u = 0 so the equations simplify to

y = ^{1}/_{2}gt^{2}

v = gt

For these examples we usually take the downward direction as positive so there is no negative sign before g
Projectiles are launched from a surface at an angle with initial velocity u. They then travel along an elliptical path in a two dimensional plane
acted on only by the force of gravity.
 The vertical and horizontal motion are independent of each other
 We can resolve the initial velocity into horizontal and vertical components
 The horizontal component is given by u_{x} = uCosΘ
 The vertical component is given by u_{y} = uSinΘ
 we can use the equation x =u_{x}t to describe the horizontal motion
 we can use the equations y = u_{y}t  ^{1}/_{2}gt^{2}
and v = u_{y}  gt to describe the vertical motion
Projectiles can be launched horizontally from a raised surface in this case the equations simplify to.
 x =u_{x}t to describe the horizontal motion
 y = ^{1}/_{2}gt^{2} and v = gt to describe the vertical motion
 In this case the downward direction is taken to be positive and y represents the distance the projectile has fallen from its initial height