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 - ¹/₂gt²
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 = ¹/₂gt²
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_xt to describe the horizontal motion
we can use the equations y = u_yt - ¹/₂gt² 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_xt to describe the horizontal motion
y = ¹/₂gt² 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