$(10$ points$)$ You are going to test drive a $2021$ Volkswagen GTI. Before heading out you decide to

look up some technical details from the owner's manual. The car has a $6$ speed manual transmission

and a maximum engine speed of $6000$ RPM$.$ The tires have an outer diameter of $637$ mm and the

differential provides a final drive ratio of $3\mathrm{.}24.$ The transmission gear ratios are given in the table.

a$)(6$ points$)$ What is the maximum speed $(k\frac{m}{h}r)$ of the car?

b$)(2$ points$)$ What is the total number of gears in the transmission? How many of them will be

rotating while the engine is running?

c$)(2$ points$)$ You are driving up a hill in $5$th gear at $2000$ RPM and trying to pass a truck in front of

you. What can you do to pass the truck more easily? Explain your answer.