Give an x-y equation for the path of the particle

[fredrick08]

Homework Statement

r(t)=(2sin(wt),3cos(wt))

a. give unit vector in direction of r'(t)
b. give unit vector in plane of motion which is normal to r'(t)
c. give an x-y equation for the path of the particle

The Attempt at a Solution

well a. i think is just finding the unit vector but i am having trouble finding it. r'/|r'|=1/root(4w^2cos^2(wt)+9w^2sin^2(wt))*r' i don't think this i right tho because i can't cancel the sin cos squared because of not common factors... and the other 2 i have no idea, please can someone help me.

 

[fredrick08]

anyone?

 

[rootX]

because of not common factors

See the question, it provides you that numbers. You cannot do much about it.

b) Hint:
r'(t).normal = 0
. = dot

c)
from r(t)=(2sin(wt),3cos(wt))
x = 2sin(wt)
y = 3cos(wt)

so find h(x) such that y = h(x)

 

[fredrick08]

thanks heaps!