$2\mathrm{.}1\mathrm{.}23.[$Level $2]$ In this problem we'll examine a two$-$

car system similar to that of Exercise $2\mathrm{.}1\mathrm{.}22.$ Again, both

cars A and $B$ are initially traveling to the right at $98f\frac{t}{s}.$ In

this case the following car has worse brakes than the car in

front, thus making it more difficult to avoid a collision when

the lead car starts braking. At $t=0$ the driver in car $B$

sees an accident taking place ahead of him and jams on his

brakes, causing a deceleration of $35f\frac{t}{s^2}.$ It takes $1$ s for the

driver of car $A$ to react to this and begin braking with a

deceleration of $30f\frac{t}{s^2}.$ The initial separation between the

cars is $30$ ft $.$ Determine whether or not car A collides with

car $B.$ If it does, what is the relative collision speed?

E$2\mathrm{.}1$