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A circle is centered at the origin and has radius of 1.5. A particle starts at point (0,1.5) and travels counterclockwise on the circle making 150 revolutions per minute. Write the parametric equations for the motion of the particle, where t represents time in minutes:

x(t) =

y(t) =

difficulty advanced
 Jun 4, 2015

Best Answer 

 #3
avatar+94545 
+10

I made a slight error, Melody [now corrected].......

 

The particle makes 1 revolution every 1/150 of a sec = 4/600 sec

 

So at  0/600   x = 0   and y = 1.5

At 1/600   x = -1/5    and y = 0

At 2/600 x = 0 and y = -1.5

At 3/600  x = 1   y = 0

At 4/600 (1/150)  x = 0    y = 1.5    right back where we started...

 

 

 Jun 4, 2015
 #1
avatar+94545 
+5

x(t)  = 1.5cos[300pi(t)]

 

y(t)  = 1.5sin [300pi(t)]

 

 

     

 

Edit....I made a slight mistake here.... the particle starts at (0, 1.5)....so.....the correct equations are actually

 

x(t)  = 1.5sin(-300pi/t)  

 

y(t) = 1.5cos(300pi/t)

 Jun 4, 2015
 #2
avatar+95334 
0

Thanks Chris,    

I shall have to think about this one.  

 Jun 4, 2015
 #3
avatar+94545 
+10
Best Answer

I made a slight error, Melody [now corrected].......

 

The particle makes 1 revolution every 1/150 of a sec = 4/600 sec

 

So at  0/600   x = 0   and y = 1.5

At 1/600   x = -1/5    and y = 0

At 2/600 x = 0 and y = -1.5

At 3/600  x = 1   y = 0

At 4/600 (1/150)  x = 0    y = 1.5    right back where we started...

 

 

CPhill Jun 4, 2015
 #4
avatar+95334 
0

Thanks Chris, I still have to think about it :))

 Jun 4, 2015

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