Answer
(a) The safe radius of curvature is $885.5~m$
(b) The safe radius of curvature is $491.9~m$
Work Step by Step
(a) We can convert the speed from units of km/h to units of m/s:
$750~km/h \times \frac{1000~m}{1~km} \times \frac{1~h}{3600~s} = 208.3~m/s$
We can find the safe radius of curvature when $a_c = 5.0~g$:
$a_c = \frac{v^2}{r}$
$5.0~g = \frac{v^2}{r}$
$r = \frac{v^2}{5.0~g}$
$r = \frac{(208.3~m/s)^2}{(5.0)(9.80~m/s^2)}$
$r = 885.5~m$
The safe radius of curvature is $885.5~m$
(b) We can find the safe radius of curvature when $a_c = 9.0~g$:
$a_c = \frac{v^2}{r}$
$9.0~g = \frac{v^2}{r}$
$r = \frac{v^2}{9.0~g}$
$r = \frac{(208.3~m/s)^2}{(9.0)(9.80~m/s^2)}$
$r = 885.5~m$
The safe radius of curvature is $491.9~m$
