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ENGR5004 / Week 1
Dynamics S2 slide 17: WE1 colliding particlesFrom lectureCurrent spec2:28 marks10 min

ENGR5004 Dynamics Session 2, slide 17 (Self Study Examples, WE1)

The motion of two particles (A and B) is described by the position vectors

rA=3t i+9t(2−t) j  (m)\mathbf r_A = 3t\,\mathbf i + 9t(2 - t)\,\mathbf j\ \ \text{(m)}

rB=3(t2−2t+2) i+3(t−2) j  (m)\mathbf r_B = 3(t^2 - 2t + 2)\,\mathbf i + 3(t - 2)\,\mathbf j\ \ \text{(m)}

with tt in seconds.

Formulas you may need
  • v=drdt=x˙ i+y˙ j\mathbf v = \dfrac{d\mathbf r}{dt} = \dot x\,\mathbf i + \dot y\,\mathbf j, speed v=x˙2+y˙2v = \sqrt{\dot x^2 + \dot y^2} (learn this)
  1. (a)
    Find the point at which the particles collide (and the time of the collision).
    [4]
  2. (b)
    Find their speeds just before the collision.
    [4]