Dynamics Projectile Motion : · v (t) = ds dt · a(t) = dv = d2s dt dt2 · V = VXT + Vy J + V2K · V= AVx+ Vy+ + V2 · a= ax+ +ay] + a2K · a= Max+ay+a2 · ay =- 9 9.81 m/s2 32.2 ft/s2 ( vertical ) · ax = 0 · Horizontal : (ax= 0) (horizontal) 4V=u+act 4 x= x0 + ut +=act2 4 v= = u2 + 2as 4> a = V-u ? · Vertical (ax =- g) 4 V- utat ? y = yo + ut +/at2 4 v2 = u2 + 205 Trajectory: vsine 1 V x = x0 + VocosOt >VCOSO y= yo + Vo sinot -1gt2 y(x) = a(x-x0)2 + b(x-x0) + yo a= - 9 2V62 cos200 b = tan 8
vsine - 7 B (20, 8) (0,4) A VOOSO 8 ft 4 ft 20ft Horizontal : 20ft Vertical: 8-4=4ft y(x)= a(x-x0)2 + b(x-x0)+yo (xo,yo)= (0,4) (x, y)=(20,8) a = - 9 , b=tano 2Vo2 cos200 8= - 32.2 2(40)2 cos20 (20-0)2 + tano (20-0) +4 : Q= 23.8°, 77.50 Curvature · radius of curvature , p = [1+(dy/dx)2]= [d?y/dx2] 0 0' (center of circle) S un P -t The n axis is always positive . Particle position: s(t) L> tangential coordinate t : a = vut + V- un 9 La intial L initial speed across t speed across n · acceleration: a = a+ Ut + an Un 4 an = v2 · a= Na+2+an2 a = \2+(x2)2
Acceleration: L> Straight line motion an= = v2 -0 a = at= v 4 Motion at constant speed a= at = v=0 so, a = an =0 unit vector 1 normal component · a = a+ ut + anun tangential component