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)

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

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 = Dt2 negative sign drops out of g equation Dt = 2Vi sinQ g Dt = 2Vy where Vyand g are both positive