Answer
(a) $0.42KN$ opposite the direction of motion.
(b) $2$
Work Step by Step
(a) We know that
$v_f^2=v_i^2+2as$
We plug in the known values to obtain:
$v=\sqrt{(0)^2-2a(0.083)}$
$\implies 54=\sqrt{(0)^2-2a(0.083)}$
$\implies a=17566\frac{m}{s^2}$
Now we can find the average force as
$F=ma$
$F=0.024\times 17566$
$F=421N=0.42KN$ opposite the direction of motion.
(b) As $a=\frac{F}{m}$
$\implies a=\frac{421}{2m}=\frac{421}{2(0.024)}=8770\frac{m}{s^2}$
We also know that
$v^2=v_i^2+2ad$
We plug in the known values to obtain:
$(0)^2=(54)^2-2(8770)d$
$\implies d=\frac{(54)^2}{2\times 8770}$
$d=0.166m$
Now the penetration depth change is $\frac{0.166}{0.083}=2$
