What is the Angle Between Velocity and Acceleration Vectors at t=(π/2w)?

[Yam]

Homework Statement

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.

Homework Equations

differentiation

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?

 

[SteamKing]

How would you normally find the angle between two vectors?

 

[haruspex]

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

 

[Yam]

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

 

[Yam]

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

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

 

[haruspex]

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

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

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