Two particles move in the xy-plane. At time t, the position of particle A is giv

Question

Two particles move in the xy-plane. At time t, the position of particle A is given by x(t) = 3 t - 3 and y(t) = 3 t - k, and the position of particle B is given by x(t) = 2 t and y(t) = t^2 - 2t - 1. (a) If k = 6, do the particles ever collide? A. yes B. no C. it is not possible to determine for certain (Be sure that you are able to explain your answer!) (b) Find k so that the two particles are certain to collide. k = (c) At the time the particle collide in (b), which is moving faster? A. particle A B. particle B C. neither particle (they are moving at the same speed)

Explanation / Answer

x1(t) = x2(t) when

3t-3 = 2t

t = 3

At t=3

y1(t) = 3*3 - 6 = 3

y2(t) = 3^2 - 2*3 - 1 = 2

y1(t) is not equal to y2(t) so the particles do not collide

b)

for collision y1(t) = y2(t) at t = 3s

3*3 - k = 3^2 - 2*3 - 1

k = 9 - 2 = 7

c) v1(t) = 3i^ + 3j^

= 3 sqrt(2) = 4.2 m/s

v2(t) = 2i^ + (2t-2)j^

v2(3) = 2i + 4j

= sqrt(20)

The velocity of particle 2 is greater during colllision

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