Answer:
754.8 m
Explanation:
The centripetal acceleration is given by
[tex]a=\frac{v^2}{r}[/tex]
where v is the speed of the airplane and r is the radius of the loop.
We can rewrite the speed of the airplane as the ratio between the length of the circumference ([tex]2 \pi r[/tex]) and the time taken:
[tex]v=\frac{2 \pi r}{t}[/tex]
Substituting in the formula of the acceleration, we have
[tex]a=\frac{(2 \pi)^2 r^2}{t^2 r}=\frac{(2 \pi)^2 r}{t^2}[/tex]
Re-arranging the formula and putting the numbers of the problem into it, we can find the radius of the loop, r:
[tex]r=\frac{at^2}{(2 \pi)^2}=\frac{(14.7 m/s^2)(45.0 s)^2}{(2 \pi)^2}=754.8 m[/tex]
