Exercise $3\mathrm{.}25$

A particle is released horizontally from A with initial velocity $u$ as shown.

a$.$ prove that the required minimum velocity $u$ is $24\mathrm{.}5\frac{m}{s}$ for the particle to reach $B.$

b$.$ find the radius of curvature $$ when the particle is at $A.$

c$.$ Calculate $r^{},{}^{},r^{}$ and ${}^{}$ from an observer at C when the particle is at $A.$

$($Answer:

$($b$)61\mathrm{.}2$ m

$($c$)-14\mathrm{.}7\frac{m}{s},0\mathrm{.}196ra\frac{d}{s},-4\frac{m}{s^2},-0\mathrm{.}00124ra\frac{d}{s^2})$