Related rates with an angle:

A particle on the x axis is moving to the right at 2 units per second. A second particle on the y axis is moving down at 3 units per second. At a certain instant, the first particle is at the point (5,0) and the second particle is at the point (0,7). How rapidly is the angle between the x axis and the line joining the two particles changing at that instant? Are the particles moving towards or away from each other at that instant?

Question

Related rates with an angle:

A particle on the x axis is moving to the right at 2 units per second.  A second particle on the y axis is moving down at 3 units per second.  At a certain instant, the first particle is at the point (5,0) and the second particle is at the point (0,7).  How rapidly is the angle between the x axis and the line joining the two particles changing at that instant?  Are the particles moving towards or away from each other at that instant?

anonymous · Answer

let Q be the angle, so, tan(Q) = y/x

anonymous · Answer

taking the derivative, sec^2(Q) = ((dy/dt)X - (dx/dt)Y) / x^2

anonymous · Answer

how to solve from there?  I get to the point of sec^2(Q) = 5/4

anonymous · Answer

actually, not sure this is right

anonymous · Answer

made a mistake, but came up with similar sec^2(Q) = 29/25

miracrown · Answer

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