$3.($TM $2-5$; $5$ pts total$)$ A jet fighter pilot knows he is able to withstand an acceleration of $9$g

before blacking out. The pilot points his plane vertically down while travelling at Mach $3$ speed

$($that is$,990$ m$/$s$)$ and intends to pull up in a circular maneuver before crashing into the ground.

You may ignore air resistance. $($Hint: you will need to consider centripetal acceleration.$)$

$($a$)(2$ pts$)$ Where does the maximum acceleration occur in the maneuver?

$($b$)(2$ pts$)$ What is the minimum radius the pilot can take?

$($c$)(1$ pt$)$ Given your answer to part $($b$),$ do the assumptions of constant gravity and constant

sound speed make sense?