$2.(7$ points$)$ Ice fishing is a popular winter

activity in many northern states. People drive

their cars out on the when the ice gets thick

enough, but there are usually one or two

accidents each winter where the vehicle goes

through ice that is too thin. You have been

tasked with analyzing this problem so that a

Public Safety Campaign can be developed to

prevent these accidents from occurring. A key

piece of this will be advising people how

serious these accidents can be$.$ You task is to

estimate how far the water can go up the door

before the door can no longer be opened. In the

scenario you are looking at the car is sinking

with the back end pointed straight down.

$($a$)(5$ points$)$ How far up the door can the water go before a person no longer be able to open the door of their vehicle while the passenger compartment is still filled with air.

$($b$)(2$ points$)$ Justify$/$explain your answer, including any assumptions that you need to make in order to solve the problem. Given the assumption you made, describe $$who$$your solution applies to$.$