# Particle on a position vector.

1. Feb 25, 2015

### Yam

1. The problem statement, all variables and given/known data
A particle moves in a plane described by the position vector r (t)= ( 2bsin( wt ))i + ( bcos( wt ) )j
where b and w are some constants. The angle between its velocity and acceleration vectors at time t=(π/2w)

a) is approximately 27 degree .
b) is exactly 45 degree .
c) is approximately 63 degree .
d) is exactly 90 degree .
e) cannot be determined since b and w are not specified.

2. Relevant equations
differentiation

3. The attempt at a solution
v(t) = (2bw(cos(wt)))i + (-bw(sin(wt))j
a(t) = (-2bww(sin(wt)))i + (-bww(cos(wt)))j

After that, how do i find the angles?

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2. Feb 25, 2015

### SteamKing

Staff Emeritus
How would you normally find the angle between two vectors?

3. Feb 25, 2015

### haruspex

What do you know about the dot product of two vectors?

4. Feb 25, 2015

### Yam

I see, the dot product would represent the angle between 2 vectors. Gimme some time to work the exact solution out

5. Feb 26, 2015

### Yam

Hi, is this formula correct? Or is this only for coordinates only?

So, the solution is Cos-1(0)=90 degrees?

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Last edited: Feb 26, 2015
6. Feb 26, 2015

### haruspex

That's the right formula, but how do you get 0 for the dot product?