Having trouble calculating Radial and Tangential aspects of a cars acceleration

[nukeman]

Having trouble calculating Radial and Tangential aspects of a cars acceleration...!

Homework Statement

Here, I will just post the question as an image. Never mind the one where I have to sketch, but b and c I am having trouble with.

How do you calculate the radial and tangential aspects of the cars acceleration? and from that info, how do I calculate the radius?

Homework Equations

 

[LCKurtz]

You have the tangential direction since you are given the velocity. Figure out the vector projection of the acceleration along the tangential direction and subtract that from the acceleration to get the normal component. From that you should be able to calculate the curvature and radius of curvature with standard formulas.

 

[nukeman]

I'm still having trouble with b

??

You have the tangential direction since you are given the velocity. Figure out the vector projection of the acceleration along the tangential direction and subtract that from the acceleration to get the normal component. From that you should be able to calculate the curvature and radius of curvature with standard formulas.

 

[SammyS]

Method 1:

Write the car's acceleration and its velocity in component form.
Then find the scalar (dot) product [itex]\vec{a}\cdot\vec{v}[/itex] from the components.
Remember that this scalar product gives you the component of a that's in the direction of v times the magnitude of v.
Can you take it from here?​

Method 2:

From the given information, find the angle between the direction of the acceleration and the direction of the velocity.
Use basic trig. to find the component of a parallel to v and the component of a perpendicular to v.​