$(20$ points$)$ The drawing shows a version of the loop$-$the$-$loop trick for a small toy car. If the car is given an initial speed of $4\mathrm{.}0\frac{m}{s},$ and the radius $r=0\mathrm{.}3m,$ what is the magnitude of normal force the rrack exerts on the car at the top point of the track? $g=9\mathrm{.}8\frac{m}{s^2}.$ Mass of the car is $0\mathrm{.}25$ kg $.$

A$.0\mathrm{.}0245$ N

B$.3\mathrm{.}92$ N

C$.0\mathrm{.}562$ N

$(10$ points$)$ Bullet with mass $m=0\mathrm{.}02kg$ and velocity $v=800\frac{m}{s}$ hits the block with mass $m_B=4\mathrm{.}5kg$ attached to a spring. The bullet stops inside the block $($buries in it$).$ Calculate the maximum compression of the spring. The spring constant $k_s=2000\frac{N}{m}.$ Assume frictionless surface.

A$.0\mathrm{.}113$ m

B$.0\mathrm{.}258$ m

C$.0\mathrm{.}168$ m

D$.0\mathrm{.}0952$ m