Circular motion- radius of the plane's vertical loop

[dani123]

Homework Statement

An 80-kg pilot flies a plane in a vertical loop. At the top of the loop, where the plane is completely upside-down for an instant, the pilot hangs freely in the seat and does not push against the seat belt. The airspeed indicator reads the 110 m/s. What is the radius of the plane's vertical loop?

Homework Equations

F_c=F_g
F_c=mV²/R

The Attempt at a Solution

So we know that m= 80kg v=110m/s and we are looking for R.
In order to do this, I simply rearranged the F_c=mV²/R equation and solved for R. And this turned out to give me R=1 235m.

I would like if someone could verify that my work here is done correctly and that the significant figures are being respected. Thank you so much for your time and help :)

 

[truesearch]

That is correct. You could also say that centripetal acceleration = v^2/R = g if there is no force on the pilot due to the seat or his seat belt. The pilot at this instant is effectively in 'free fall'