I need help with part(a). I can find the parametric equations for a nonmoving ladder, but when the ladder begins to move i'm having difficulty.
http://www2.palomar.edu/users/canfin...0Equations.pdf
I need help with part(a). I can find the parametric equations for a nonmoving ladder, but when the ladder begins to move i'm having difficulty.
http://www2.palomar.edu/users/canfin...0Equations.pdf
at time 't' the point A is at (3t,0). let the point B be at (0,y(t)) at time 't'. Then why?
this will give you the coordinated of point B with time. Find the coordinates of M using the above. now the monkey is at a distance of from M.(why?)
can you now locate the coordinates of the monkey at time 't'. That when done will give you the required parametric equation.
The coordinates of A at time 't' will be
Let the coordinates of B at time 't' be (i am purposely not using y(t) you will see why.)
The equation of the line AB at time 't' is given by :
.(do you see why?)
The coordinates of M at time 't' are:
(why?)
The monkey is at a distance of 2t from M so the monkey will be found somewhere on the circle centred at M and of radius 2t.(make sure you understand why this is so). At the same time the monkey is also on the ladder,that is, the monkey will also be somewhere on line AB. The intersection of the circle (mentioned above in green) and AB will give you the position of the monkey.
The equation of that circle is .
This will intersect AB at two points. One of these is the position of the monkey. Can you figure out which one.
With slight changes the correct solution is:
The coordinates of A at time 't' will be
Let the coordinates of B at time 't' be (i am purposely not using y(t) you will see why.)
The equation of the line AB at time 't' is given by :
.(do you see why?)
The monkey is at a distance of 2t from A so the monkey will be found somewhere on the circle centred at A and of radius 2t.(make sure you understand why this is so). At the same time the monkey is also on the ladder,that is, the monkey will also be somewhere on line AB. The intersection of the circle (mentioned above in green) and AB will give you the position of the monkey.
The equation of that circle is .
This will intersect AB at two points. One of these is the position of the monkey. Can you figure out which one?
Once I find b(t) using that equation, do I plug b(t) into the y= -b(t)x/3t + b(t) equation to get y in terms of x and t?
I'm a little confused on what I do next. Now that b(t) is not really y, where am I suppose to get my 2 parametric equations from?
I have y = (- (144-9t^2)^.5 )*x/(3t) + (144 - 9t^2)^.5
I took b(t) and plugged it into the equation of the line AB.
to find the intersection of the circle and the line you of course need their corresponding equations.
the equations of them are :
1)Line AB: . (plug in b(t) you have found out. i would advice that you find the coordinates of Monkey(M) in terms of b(t) and then plug in the b(t) you have found out.)
2) circle:
solve the above two equations simultaneously to get x= some whacky expression in 't'; y= another whacky expression in 't'. these are the coordinates of the monkey.
now is it clear ?