# 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 ux = uCosΘ
• The vertical component is given by uy = uSinΘ
• we can use the equation x =uxt to describe the horizontal motion
• we can use the equations y = uyt - 1/2gt2 and v = uy - gt to describe the vertical motion

Projectiles can be launched horizontally from a raised surface in this case the equations simplify to.

• x =uxt 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