Relative motion

Hello

 

 

at this problem

 

 

 

 

the car is moving around the circle with constant speed , and it is asking for

 

 

d^2R/dt^2 for the radar

 

And

 

d^2(theta)/dt^2 for the radar

 

at the instance the speed of car is vertical downwards as shown

 

 

the speed equals 120 km/hour

 

And the radius of the circle is 450

 

 

so I said

 

a® = (d^2R/dt^2) - R (omega^2)

 

but the only acceleration is the central which equals (v^2/ Radius) and in the same direction

 

so we can get d^2R/dt^2 .

 

and when I try to get the (alpha)(d^2 theta / d t^2)

 

a (theta) = R*(alpha) + 2 (omega)* (dR/dt)

 

 

and a(theta) equals zero

 

and here is my question , what is the value of dR/dt ???

 

I think it has to be zero , since the velocity is vertical and the unit vector R cap is horizontal

 

so

 

1- Is Alpha zero ?

 

2- can dR/dT equal zero at that situation , while d^R/dt^2 has a value ?

 

I think no problem but I wanted to make sure I'm right in this solution