Problem $2$: $50$ pts Two Vehicles, A and B$,$ are driving along a straight downhill road with a slope of $3\%.$ The distance between the two cars is initially $500$ feet. Both cars are traveling at a speed of $60$ mi$/$h $(88$ ft$/$s$)$ when suddenly, Vehicle A sees an obstacle $500$ feet ahead and immediately applies full brakes to stop. Vehicle B$,$ however, does not start braking until it sees that Vehicle A has come to a complete stop. Vehicle B also brakes as soon as it realizes that A has stopped. $1.$ Calculate whether Vehicle A will be able to stop before hitting the obstacle. Assume A$\text{'}$s driver has a perception$-$reaction time of $1\mathrm{.}5$ seconds. $(20$ pts$)2.$ After Vehicle A has completely stopped, B begins braking. Vehicle B$\text{'}$s driver is an elderly driver with a perception$-$reaction time of $2\mathrm{.}5$ seconds. Calculate whether Vehicle B will collide with Vehicle A$.(30$ pts$)3.$ Self$-$driving technology is often considered safer than human drivers. Using the case of Car A and Car B$,$ describe how self$-$ driving systems could improve safety. Specifically, explain which aspects of driving can be enhanced by autonomous technology and how this could have prevented the collision in the given case? $($Bonus $10$ pts