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denpristay [2]
3 years ago
6

Two particles are traveling through space. At time t the first particle is at the point (−1 + t, 4 − t, −1 + 2t) and the second

particle is at (−7 + 2t, −6 + 2t, −1 + t). (a) (5 Points) Do the paths of the two particles cross? If so, where?
Physics
1 answer:
Pie3 years ago
5 0

Answer:

Yes, the paths of the two particles cross.

Location of path intersection = ( 1 , 2 , 3)

Explanation:

In order to find the point of intersection, we need to set both locations equal to one another. It should be noted however, that the time for each particle can vary as we are finding the point where the <u>paths</u> meet, not the point where the particles meet themselves.

So, we can name the time of the first particle T_F ,  and the time of the second particle T_S.

Setting the locations equal, we get the following equations to solve for T_F and T_S:

(-1 + T_F) = (-7 + 2T_S)                     Equation 1

(4 - T_F) = (-6 + 2T_S)                        Equation 2

(-1 + 2T_F) = (-1 + T_S)                     Equation 3

Solving these three equations simultaneously we get:

T_F = 2 seconds

T_S = 4 seconds

Since, we have an answer for when the trajectories cross, we know for a fact that they indeed do cross.

The point of crossing can be found by using the value of T_F or T_S in the location matrices. Doing this for the first particle we get:

Location of path intersection = ( -1 + 2 , 4 - 2 , -1 + 2(2) )

Location of path intersection = ( 1 , 2 , 3)

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