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Introductory Physics Homework Help
What Angle Causes Particles A and B to Collide?
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[QUOTE="BeyondBelief96, post: 6044818, member: 649089"] [h2]Homework Statement[/h2] A particle A moves along the line y = d (30 m) with a constant velocity [ATTACH=full]229683[/ATTACH] (v= 3.0 m/s) directed parallel to the positive x-axis (Fig. 4-40). A second particle B starts at the origin with zero speed and constant acceleration [ATTACH=full]229681[/ATTACH] (a = 0.40 m/s2) at the same instant that particle A passes the y axis. What angle θ between [ATTACH=full]229682[/ATTACH] and the positive y-axis would result in a collision between these two particles?[/B][h2]Homework Equations[/h2] Kinematic Equations[h2]The Attempt at a Solution[/h2] So I listed out all knowns and unknowns for both particle A & B as follows: Particle A: Xi = 0, Xf = ?, Vix = 3 m/s, Vif = 3m/s, a = 0 t = ? and y = 30 Particle B: Xi = 0, Xf = ?, Vix = 0 m/s, Vif = ?, ax = asin(theta), t = ? Yi = 0, Yf = 30, Viy = 0 m/s, Vif = ?, ay = acos(theta), t = ? From there I used the kinematic equation d = vit + 1/2at^2 for particle A and B and got the following: Particle A: x = 3t, y =30 Particle B: x = 1/2asin(theta)t^2, y = 1/2acos(theta)t^2 I set each of the equations equal to each other and tried to solve the system of equations for theta as follows: 3t = 1/2asin(theta)t^2 (Eq1) 30 = 1/2acos(theta)t^2 (Eq2) [B]3 = 1/2asin(theta)t so t = 6/asin(theta)[/B] [B] So I plugged t into Eq2: 30 = 1/2acos(theta)[6/asin(theta)]^2 from here I am at a loss on how to solve for theta. To be honest, my algebra solving skills arent super spectacular, which is a bit sad haha. I was able to simplify this as: 30 = 1/2acos(theta)[36/a^2sin^2(theta)] == 5/3 = cot(theta)/asin(theta) ...aaaaaand this is where I am lost.[/B][/B] [/QUOTE]
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Introductory Physics Homework Help
What Angle Causes Particles A and B to Collide?
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