Question

Suppose that the position of one particle at time t is given by the equations Xy and y1. Meanwhile, the position of a second particle is given by the equations 2 and Y2 X1 - 3sin() Yi - 2cos(t) Osts 21 2-3 + cos(0) Y2 - 1 + sin(1) Osts 2x (a) Graph the paths of both particles. (Do this on paper. Your instructor may ask you to turn in this work.) How many points of intersection are there? (b) Find the collision point, where the particles are at the same place at the same time. (c) Ir the x-coordinate of the second particle is given by x2 - 3 + cos(t) instead, is there still a collision? Yes O No

Answer 1

7,23 sint Y = 2 cost ostez 2 y = Sinti sa Se a Cost know sint4 costa so Gj?+41 ar is the equation och parabola maior axis along 'x'axis at rough Sketch is wills to 630) 6,-2) --3+ cost • ₂ = 1t sint oster ^2 +3 = Cost 42-12 sint It is of Circle wills Center (22+23€ (I v² z equation (arengte awt=1 [-(-1)]²+ )" is (-3,0) center Center Rough sketch

these Combining graph get AY (0,2) tov (30) >x (-3,0) 10,-2) Heace the .یه) graphy Wir Meat two points It we draw bola figures in Desme tool we got graphing Point of Intersections are 620) (-2.097,1-43) Graphing sketch is shown below. so Collision points are (-3,0), 162.097,843) If A = 3tlost y=1t sind L 22-0)2+ if (It) a lhen ar is Creation of Cirlle wils Center (3,1) ins rough skeren will be (0,214 3,1) (3,0) Yes there is Still Gllision 124

111 & (0, 2) a (-2.097, 1.43) -4 -2 0 2 4 (-3,0) + ( )2 + (*)=1 2 X (x + 3)2 + (y - 1)2 = 1 3 powered by desmos