SOLUTION: a point is moving along the positive y axis at a constant rate of 6 units per second. Find the rate of change of its distance from (1,0) when y=2 Thank you

Algebra ->  Finance -> SOLUTION: a point is moving along the positive y axis at a constant rate of 6 units per second. Find the rate of change of its distance from (1,0) when y=2 Thank you      Log On


   

Question 1120315:
a point is moving along the positive y axis at a constant rate of 6 units per second. Find the rate of change of its distance from (1,0) when y=2
Thank you
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Don't get too lost in the forest because of the trees....

The statement of the problem gives you the answer. The speed is constant at 6 units per second; so the rate of change of its distance from ANY point at ANY time is 6 units per second.

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sorry -- I misread the problem as motion in one dimension.

See the correct solution from tutor @ikleyn.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

I am here to fix an error in the @greenestamps solution. 

The distance from the point (0,y), moving along the y-axis, to the point (1,0) fixed in the coordinate plane, is  D = sqrt%28y%5E2%2B1%29   (Pythagoras).


The rate of the distance change is the derivative 


%28dD%29%2F%28dt%29 = %281%2F2%29%2A+%282%2Ay%2A+%28%28dy%29%2F%28dt%29%29+%2F+sqrt%28y%5E2%2B1%29%29 = y%2A+%28%28dy%29%2F%28dt%29%29+%2F+sqrt%28y%5E2%2B1%29 = 


    now substitute the given value of y= 2 and the given rate  %28dy%29%2F%28dt%29 = 6 into the formula to get the rate of the distance change = 


= %282%2A6%2Fsqrt%281%2B2%5E2%29%29 = 12%2Fsqrt%285%29 units per second.


Answer.  The rate of the distance change = 12%2Fsqrt%285%29 units per second.