$3)$In "the trolley problem" in ethics, the philosopher Philippa Foot posed the following scenario:A trolley $($a one$-$car train$)$ is running out of control down a track. In its path are five people who have been tied to the track by a mad philosopher. You could choose to flip a switch, which will lead the trolley down a different track.Unfortunately, there is a single person tied to that track. Should you flip the switch or do nothing?"W$**!"$ you say, $"$I$\text{'}$m a physics student! I$\text{'}$m not going to settle for killing fewer people. I$\text{'}$m going to save them all!" A third track $($unnoticed by Foot$)$ leads to the hills shown in the sketch. You consider switching the trolley $($which has a mass of $1600$ kg$)$ onto this track instead. If you do so$,$ the trolley will start at a speed of $35\mathrm{.}0$ m$/$s at the top of a hill that is $30$ meters tall. It will then race to the ground below, go through a circularly curved section with a $40$ m radius of curvature, then coast up the next hill, the top of which is $60$ meters above the ground. In an attempt to stop the trolley, the driver has put on the brakes full strength locking the wheels, so that they don't turn. However, there are wet leaves on the track, so that the friction with the track is negligible, except for a section that is $25$ m long after the second hill, with coefficient of kinetic friction $0\mathrm{.}78.$ After this section, the trolley will slide frictionlessly along a levelstretch of tracks until it hits a massless spring with k $=100$ N$/$m$.$ Without compression, the spring extends $150$ m froma wall, as shown. There is a student tied to the tracks $60$ m from the wall. Neglect air resistance. Treat the trolley as a point mass.a$)$ Where, relative to the wall, would the trolley come to a stop? Would the student be injured? Should you switch the trolley to this track?$(7$ points$)$b$)$ At the bottom of the circularly curved section $($the lowest point on the track$),$ what is the force exerted upward by the track on the trolley, assuming you do switch it to this track.