When an aircraft takes off, it accelerates until it reaches its takeoff speed v. in doing so it uses up a distance r of the runway, where r is proportional to the square of the of the takeoff speed. if v is measured in miles per hour and r is measured in feet, then 0.1639 is the constant of proportionality. if an aircraft has a takeoff speed of about 215 miles per hour, how much runway does it need?

 36.22 feet

Explanation:

Two quantities are proportional if and only if their ratio is constant. Since V and the square of R are proportional, then the ratio of V to the square of R is constant. In terms of equation:



For some constant k.

Since the constant of proportionality is equal to 0.1639, k = 0.1639. Moreover, since the takeoff speed of the aircraft needs to be 215 miles per hour, the runway needed is will be obtained by solving for R in the following equation:



Hence, a runway of 36.22 feet is needed for the aircraft to have a takeoff speed of 215 miles per hour.

 

I'm pretty sure it's b). i try drawing the functions out and b is the one that stands out or isnt a "line"