The jet comes in for a landing on solid ground with a speed of $100\frac{m}{s},$ and its acceleration can have a maximum magnitude of $5\frac{m}{s^2}$ as it comes to rest. $($a$)$ From the instant the jet touches the runway, what is the minimum time interval needed before it can come to rest? $($b$)$ Can this jet land at a small tropical island airport where the runway is $0\mathrm{.}8km$ long? $($c$)$ Explain your answer.