PROJECTILES LAUNCHED AT AN ANGLE PROJECTILE MOTION EQUATIONS HORIZONTAL MOTION

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 PROJECTILE MOTION EQUATIONS 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 = √ Vi2sinQ2-(2gDy) from Dy = ViDt - ½(gDt2) Dy = VisinQDt -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 2 sinQcosQ

3. PROJECTILES LAUNCHED AT AN ANGLE PROJECTILE MOTION EQUATIONS Dt for total trip of projectile at landing where Dy = 0 from Dy = VisinQDt - ½(gDt2) 0 = VisinQDt - ½(gDt2) Dy = 0 at end of trip - VisinQDt = - ½(gDt2) using algebra 2VisinQDt = Dt2 negative sign drops out of g equation Dt = 2VisinQ g Dt = 2Vywhere Vyand g are both positive g