# Vectors

• Mar 15th 2009, 11:15 AM
djmccabie
Vectors
A particle P moves such that its position vector r with respect to the origin O at the time t is given by

r = cos3ti + sin3tj

a) Find an expression for v, the velocity of P at time t.

b) Show that the direction of v is perpendicular to that of r for all values of t.

c) Find the speed of P.

OK for part a I'm assuming you differentiate r which i get

v = -3sin3ti + 3cos3tj

is this correct??Part b Im stumped with, not sure I've learned that.

For part c i think maybe i use equation v=u+at ??
if so how could i find t ?
• Mar 15th 2009, 11:41 AM
TheEmptySet
Quote:

Originally Posted by djmccabie
A particle P moves such that its position vector r with respect to the origin O at the time t is given by

r = cos3ti + sin3tj

a) Find an expression for v, the velocity of P at time t.

b) Show that the direction of v is perpendicular to that of r for all values of t.

c) Find the speed of P.

OK for part a I'm assuming you differentiate r which i get

v = -3sin3ti + 3cos3tj

is this correct??Part b Im stumped with, not sure I've learned that.

For part c i think maybe i use equation v=u+at ??
if so how could i find t ?

For part b) we know that if two vectors are perpendicular that the dot product is zero... so

$\vec r \cdot \vec v=(\cos(3t)(-3\sin(3t))+(\sin(3t)(3\cos(3t)=0$

Speed is the magnitutde of velocity so...

$\sqrt{\vec v \cdot \vec v}=...$
• Mar 15th 2009, 11:42 AM
djmccabie
thanks pal. Did i do part a correctly?
• Mar 15th 2009, 11:57 AM
TheEmptySet
yes