Chapter 23, Problem 22P

A plane is being tracked by radar, and data are taken every second in polar coordinates $\theta$ and r.

t, s,	200	202	204	206	208	210
θ, rad	0.75	0.72	0.70	0.68	0.67	0.66
r, m	5120	2370	5560	5800	6030	6240

At 206 s, use the centered finite difference (second-order correct) to find the vector expressions for velocity $\stackrel{\to }{v}$, and acceleration $\stackrel{\to }{a}$. The velocity and acceleration given in polar coordinates are:

$\stackrel{\to }{v}=\stackrel{\dot{}}{r}{\stackrel{\to }{e}}_r+r\stackrel{\dot{}}{\theta }{\stackrel{\to }{e}}_{\theta }$ and $\stackrel{\to }{a}=\left(\ddot{r}-r{\stackrel{\dot{}}{\theta }}^2\right){\stackrel{\to }{e}}_r+\left(r\ddot{\theta }+2\stackrel{\dot{}}{r}\stackrel{\dot{}}{\theta }\right){\stackrel{\to }{e}}_{\theta }$