Problem #$3$: Absolute and Relative Motion

A car is driving in circles with a radius of $20[m].$ At this instant the car has a speed of $v_B=10[\frac{m}{s}]$ and is located at point $"$ B $",$ see the diagram below which shows the car as seen from above. At this instant, $=135$ and ${}^{}=3[ra\frac{d}{se{c}^2}].$

At the same time a bicyclist, at point $"A"$ is moving along a straight line path with a speed of $]$ and is$,$ at the same instant braking, so they are reducing their speed by $1[\frac{m}{s^2}],$ see the diagram which shows the situation as seen from above.

Determine the following:

a$)$ vec$(v{)}_A$ written in hat$(u{)}_t$&hat$(u{)}_n$ components

b$)$ vec$(v{)}_B$ written in hat$(u{)}_r$&hat$(u{)}_{}$ components

c$)$ vec$(v{)}_{\frac{B}{A_{\text{r}\text{e}\text{l}}}}$ written using $AN{Y}_{?}$ defined unit vectors

d$)$ vec$(v{)}_{\frac{A}{B_{\text{r}\text{e}\text{l}}}}$ written in hat$(u{)}_t$&hat$(u{)}_n$ components

e$)$ vec$(a{)}_A$ written in hat$(u{)}_t$&hat$(u{)}_n$ components

f$)$ vec$(a{)}_B$ written in hat$(u{)}_r$&hat$(u{)}_{}$ components

g$)$ vec$(a{)}_{\frac{B}{A_{\text{r}\text{e}\text{l}}}}$ written using $AN{Y}_{?}$ defined unit vectors

h$)$ vec$(a{)}_{\frac{A}{B_{\text{r}\text{e}\text{l}}}}$ written in hat$(u{)}_t$&hat$(u{)}_n$ components

i$)$ hat$(u{)}_r$ written in hat$(u{)}_t$&hat$(u{)}_n$ components