Answer
$(a)$ $F=k\frac{ws^2}{r}$
$(b)$ $s_2=48mi/h$
Work Step by Step
$(a)$ According to the information given in the problem, we can write the equation:
$F=k\frac{ws^2}{r}$
Where $k$ is the constant of proportionality.
$(b)$
For the first car:
$F_1$ is unknown
$w_1=1600 lb$
$s_1=60mi/h$
$k$ is unknown
For the second car:
$F_2$ is unknown
$w_2=2500lb$
$s_2$ is unknown
$F_1=F_2$
$F_1=\frac{k(1600)\times60^2}{r}$
$F_2=\frac{k(2500)\times {s_2}^2}{r}$
$\frac{k(1600)\times60^2}{r}=\frac{k(2500)\times {s_2}^2}{r}$
$k(1600)\times60^2=k(2500)\times {s_2}^2$
$2500{s_2}^2=1600\times60^2$
$25{s_2}^2=16\times3600$
${s_2}^2=2304$
$s_2=48mi/h$