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If two objects travel through space along two different curves If two objects tr

ID: 2965761 • Letter: I

Question

If two objects travel through space along two different curves

If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions for t > 0. Find the values of t at which the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Explanation / Answer

The Particals will collide when they are at Same Point

Therefore

the Coordinates Become Equal

Therefore

t^2 = 8t - 7

t^2 - 8t + 7 = 0

(t-1)(t-7) = 0

t = 1 , 7 -----------------(1)

Also

3t - 2 = t^2

t^2 - 3t + 2 = 0

(t-1)*(t-2) = 0

t = 1 , 2 ...........................(2)

Also

t^2 = 5t - 4

t^2 - 5t + 4 = 0

(t - 1)(t - 4) = 0

t = 1 , 4 --------------------------(3)

From Eq(1) ,(2) and (3) ,we get common values of t

t = 1