Vectors question D:

[lzxnl]

Think of vectors almost like paths. The vector AB then is a vector linking A to B. A position vector merely links the object's coordinates with the origin. The velocity vector is defined through a difference quotient similar to how scalar derivatives are defined; as there is a r(t+h)-r(t) term, the direction of the velocity vector is the direction of motion at that time. Likewise with acceleration.
For finding resolutes, just remember that when finding the vector resolute of a in the direction of b, you want some scaled vector kb such that (a-kb), a and (kb) form a right angled triangle; (a-kb).kb=0.
There's really not that much to vectors in the spesh course.

it's kinda common sense... sorry if that makes you feel bad! but then again it's taught in both the MUEP and UMEP maths courses.

Anyways here's a pretty diagram to try help explain it

(Image removed from quote.)
Yes a circle does work since it says constant speed. Actually, so does any random path so long as it maintains a constant speed.
@Rhubarb, you're right if the question said constant velocity, then it's linear

But let's all pretend it's linear and duquesne is right  -makes our lives a whole lot easier. Or nliu, find the circular path and solve it for us (infinite soln if its circular i think)

Helical paths (:

[jono88]

Can someone explain how Lami's Theorem works? I'm still not 100% confident of it. Linking it to question 7 exam 1 2011 would be useful.

[revcose]

Did you have a look at wikipedia's entry on it? I think it's quite clear. Essentially you use the sine rule, but instead of a triangle, you have three lines coming out of a point. The magnitude of each vector divided by the sine of the angle between the two other vectors will be the same.

In 7b from 2011-1, it is asking what m is when the magnitude of T2 is 98. From Lami's Theorem:
(m*g)/sin(90deg) = 98/sin(150deg) [=T1/sin(120deg)]
(m*g)/1 = 98/(1/2)
m = 196/g
m = 20