restart: Joel Mayes Project #2 Yasskin, Math 152-201 with(plots): with(plottools): a:=eval(2*sin(0.5*x),x=3): b:=evalf(-3*Pi/2): ball:=disk([2.8,a+0.48],1/2,color=gold): sun:=disk([-4,2.5],1,color=yellow): p1:=display(ball): p2:=plot(2*sin(0.5*x),x=b..3.14,y=-3.14..3.14,color=blue): f1:=display(p1,p2): p4:=translate(p1, -.25,-.05): f2:=display(p2,p4): p5:=translate(p4,-.25,-.08): f3:=display(%,p2): p6:=translate(p5,-.25,-.09): f4:=display(%,p2): p7:=translate(p6,-.25,-.11): f5:=display(%,p2): p8:=translate(p7,-.25,-.14): f6:=display(p2,p8): p9:=translate(p8,-.25,-.16):f7:=display(p2,p9): p10:=translate(p9,-.25,-.18): f8:=display(p2,p10): p11:=translate(p10,-.25,-.21): f9:=display(p2,p11): p12:=translate(p11,-.25,-.23): f10:=display(p2,p12): p13:=translate(p12,-.25,-.24): f11:=display(p2,p13): p14:=translate(p13,-.25,-.25): f12:=display(p2,p14): p15:=translate(p14,-.25,-.26): f13:=display(p2,p15): p16:=translate(p15,-.25,-.25): f13:=display(p2,p16): p17:=translate(p16,-.25,-.21): f14:=display(p2,p17): p18:=translate(p17,-.25,-.245): f15:=display(p2,p18): p19:=translate(p18,-.25,-.23): f16:=display(p2,p19): p20:=translate(p19,-.25,-.22): f17:=display(p2,p20): p21:=translate(p20,-.25,-.21): f18:=display(p2,p21): p22:=translate(p21,-.25,-.19): f19:=display(p2,p22): p23:=translate(p22,-.25,-.15): f20:=display(p2,p23): p24:=translate(p23,-.25,-.12): f21:=display(p2,p24): p25:=translate(p24,-.25,-.08): f22:=display(p2,p25): p26:=translate(p25,-.25,-.06): f23:=display(p2,p26): p27:=translate(p26,-.25,-.02): f24:=display(p2,p27): p28:=translate(p27,-.25,.03): f25:=display(p2,p28): p29:=translate(p28,-.25,.08): f26:=display(p2,p29): p30:=translate(p29,-.25,.12): f27:=display(p2,p30): p31:=translate(p30,-.25,.12): f28:=display(p2,p31): p32:=translate(p31,-.25,.15): f29:=display(p2,p32): head:=circle([-4,-7/4],1/4): body:=line([-4,-2],[-4,-11/4]): leg1:=line([-4,-11/4],[-7/2,-3]): leg2:=line([-4,-11/4],[-9/2,-3]): arm1:=line([-4,-9/4],[-7/2,-2]): arm2:=line([-4,-9/4],[-9/2,-2]): b1:=display(head, body, arm1, arm2, leg1, leg2,line([-5,-3],[5,-3],color=brown)): sun:=disk([3,2.5],1,color=yellow): g(x):=-.29*x^2+2.8: if30:=translate(p32,8,0): f30:=display(b1,sun,if30): g1:=plot(-.29*x^2+2.8,x=b..3.14,y=-3.14..3.14): y:=x->-.29*x^2+2.8: ball:=x->disk([x,y(x)],1/2,color=gold): ball:= proc(x,y) plots[pointplot]([[x,y]],color=gold, symbol=solidcircle,symbolsize=80) end proc: smash1:=animate(ball, [x,y(x)], x=3.5..0, scaling=constrained, axes=none, frames=20): f30:=display(smash1,b1,sun): b2:=display([b1,point([-3.65,-1.5]),point([-3.4,-1.75]),point([-3.5,-1.9]),point([-4.35,-1.5]),point([-4.5,-1.75]),point([-4.4,-1.9]),circle([-4,-1.85], 1/15)]): smash2:=animate(ball, [x,y(x)], x=0..-3.75, scaling=constrained, axes=none, frames=20): f31:=display(smash2,b2,sun): head2:=ellipse([-4,-2.5],.4,.2,color=red): body2:=translate(body, 2,0): leg3:=translate(leg1,0,0): leg4:=translate(leg2, -.5,-.05): arm3:=translate(arm1,-.5,0-.65): arm4:=translate(arm2,-.35,-.7): b3:=display(head2,leg3,leg4,arm3,arm4,line([-4.3,-3],[-3.5,-2.75]),line([-5,-3],[5,-3],color=brown),point([-3.65,-2.95],color=red),point([-3.4,-2.75],color=red),point([-3.5,-2.8],color=red),point([-4.35,-2.75],color=red),point([-4.5,-2.9],color=red),point([-4.4,-2.8],color=red),sun): f32:=b3: display([f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18,f19,f20,f21,f22,f23,f24,f25,f26,f27,f28,f29,f30,f31,f32], insequence=true, scaling=constrained, axes=none); This short animation utilizes several features of physics including force of gravity that causes the ball to roll down the hill, projectile motion, and collisions (in this case, a very inelastic collision). Best viewing speed is about 24 frames per second.