How to find acceleration from velocity, coefficient of kinetic friction and radius of curvature I've been going through the various sections of my Engineering Dynamics HW and I've been struggling to solve this problem for a while:

A car is travelling at a speed of 30 m/s at the top of a hill at a given instant. The coefficient of kinetic friction between the tyres and the road is 0.8. The instantaneous radius of curvature of the car’s path is 200 m. If the driver applies his brakes and the wheels lock, what is the resulting deceleration of the car tangent to its path?

I already know that $$\vec{a}=\frac{d\vec{v}}{dt}$$ And that $$\mu=\frac{\vec{F}}{\vec{F_N}}$$ But I'm unsure how the radius of curvature plays into the problem, and how to decompose the resultant vector acceleration into tangential and normal components.
I do not want the solution, rather assistance with the concepts and finding the equation that will answer the problem.
 A: 
But I'm unsure how the radius of curvature plays into the problem, and how to decompose the resultant vector acceleration into tangential and normal components.

The radial (normal) component points towards/away from the center of the circle. The tangential component points tangent to the circle, perpendicular to the radial component. At the top of a circular hill this just means that radial is up or down and tangential is left or right.
Using this you can just apply Newton's second law to each component like one does in most introductory Newton's second law problems:
$$F_{\text{rad,net}}=ma_\text{rad}$$
$$F_{\text{tan,net}}=ma_\text{tan}$$
The radial acceleration (sometimes called centripetal acceleration) depends on the radius of the circular path (an equation for this should be derived/given to you), and of course you are asked to find the tangential acceleration.

I already know that $$\mu=\frac{\vec{F}}{\vec{F_N}}$$

Small note here, but you can't divide by a vector. The simplified model of friction just relates magnitudes of the friction and normal forces
$$F_\text{friction}=\mu F_\text{N}$$
$$\mu=\frac{F_\text{friction}}{F_\text{N}}$$
One could write out a vector equation where $\mathbf F_\text{friction}$ is a vector of magnitude $\mu F_\text{N}$ perpendicular to $\mathbf F_\text{N}$, but it's probably more trouble than it's worth.
