How to get the normal acceleration

Question

For the problem below, I tried solving it, but I don't know where I should get the value of normal acceleration, guess I was lost.

And here's what I solved so far

Answer 1

You are almost there.

In order to calculate the tangential and the normal acceleration you need to take them as vectors.

The angles are

• $\theta= \arctan(16/12)=-53.13 deg$ for velocity
• $\phi= \arctan(16/12)=-26.51 deg$ for accelaration

Therefore the vectors for acceleration and velocity would be

And then you can find the component of tangential and normal acceleration as:

• tangential: $a_t =a \cos(\theta-\phi)$
• normal: $a_n =a \sin(\theta-\phi) = 5\frac{m}{s^2}$

Then you can just substitute:

$$R = \frac{v^2}{a_n}= \frac{20^2}{5}= \frac{400}{5}= 80 in$$