question for the true spesh genius!

[sachinmachin]

Part cii has got me stumped....rest is okay but relevant to that part
question 2
Let C = ai+bj and let R represent the position of an object which moves such that R.(R-C) = 0.
part a) Find, in terms of a and b, the cartesian equation of the path of the moving object.

part b) Describe the shape of the path and its key features,

part ci) show that R = (pcos(qt) + c)i + (psin(qt) + d)j represents the motion of a particle moving in a circle at constant speed, where p,q, c and d are constants.

??part cii)?? Hence find a vector equation to represent the motion of the object if C = 40i and the object is initially at C and travels at a constant speed of 3m/s in an anticlockwise direction.

[Mao]

let



This is a circle centered the midpoint between origin and C with diameter of |C|. O and C are two ends of a diameter, and OCR makes a right-angled triangle (this is true for any circumscribed triangle that has the diameter as a side).

, where (T is the period)

C has been specified to be 40i, hence
The circumference is , the period is the circumference divided by speed, which is also obtainable from q, hence

Hence

[sachinmachin]

thanx a lot...
mao can do no wrong..
is this is an easy question though? in terms of vector calculus??
could i expect something like this on the exam??

[Mao]

Yes you can.

This question isn't particularly easy, but it is fair.

[sachinmachin]

one question Mao.
how does the value of C = 40. Would this not be considered as the radius rather than the diameter. as 40i runs along the the positive x-axis??

[Mao]

one question Mao.
how does the value of C = 40. Would this not be considered as the radius rather than the diameter. as 40i runs along the the positive x-axis??

C is the diameter.

[believe_in_you]

I dont get how you get b ! Can you help me pls ?

I am not good at Math at all