Question

Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle. At the bottom of the dive, the speed of the airplane is 390 m/s. What is the smallest radius allowable for the vertical circle if the pilot's apparent weight is not to exceed 5.0 times his true weight?

Answer 1

$$N-mg=\frac{mv^2}{r}$$

$$5mg-mg=\frac{mv^2}{r}\\4g=\frac{v^2}{r}\\4(9.8)=\frac{390^2}{r}$$

$$r= 3900\ m$$