1. PROJECTILES LAUNCHED AT AN ANGLE PROJECTILE MOTION EQUATIONS
HORIZONTAL MOTION
Vx = velocity in horizontal
direction given Vi, q
Vx = Dx/ Dt Dx = Vx Dt
Dx = distance in horizontal
direction given Vi, q, Dt
Dt =
ANGULARLY LAUNCHED
VERTICAL MOTION
OBJECT WITH INITIAL VELOCITY (Vi ≠0)
Vy = velocity in vertical direction
given Vi, q
from Vf = Vi - gDt
Vfy = VisinQ - (gDt) velocity at midpoint = 0 (Vy =0)
and Dt is ½ (half)

2. PROJECTILES LAUNCHED AT AN ANGLE
PROJECTILE MOTION EQUATIONS
from Vf = √(Vi2 + 2aDy)
Vfy = √ Vi2sinQ 2-(2gDy)
from Dy = Vi Dt - ½(gDt2)
Dy = VisinQ Dt -1/2(gDt2)
at midpoint Vy = 0 and Dt = 1/2
Vy = VisinQ - (gDt) = 0 and Dt = Dx/VicosQ
VisinQ = (gDt) using algebra
VisinQ = 1/2(gDt) at midpoint Dt = 1/2
Vi = 1(gDt) using algebra
2 sinQ
Vi = 1(gDx) substituting Dt
2 sinQVicosQ
Vi 2 = (gDx) using algebra
2 sinQcosQ
Vi = SQRT (gDx) initial velocity givenDx, Q

3. PROJECTILES LAUNCHED AT AN ANGLE
PROJECTILE MOTION EQUATIONS
Dt for total trip of projectile at landing where Dy = 0
from Dy = Vi sinQDt - ½(gDt2)
0 = Vi sinQDt - ½(gDt2) Dy = 0 at end of trip
- Vi sinQDt = - ½(gDt2) using algebra
2Vi sinQDt = Dt negative sign drops out of
g equation
Dt = 2Vi sinQ g
Dt = 2Vy where Vyand g are both positive