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 320 m/s. What is the smallest radius allowable for the vertical circle if the pilot's apparent weight is not to exceed 7.00 times his true weight?
A) 1740 m
B) 1490 m
C) 2240 m
D) 228 m
E) 41.7 m

Question

Quizplus · Accepted Answer

At the bottom of the loop, the pilot's apparent weight is the vector sum of his true weight mg and the centripetal force mv^2/r. For the pilot's apparent weight not to exceed 7.00 times his true weight, we must have:$$mg+mv^2/r\le7mg$$$$v^2/r\le6g$$$$r\ge v^2/6g$$$$r\ge(320	ext{ m/s})^2/(6	imes9.8	ext{ m/s}^2)=\boxed{1740	ext{ m}}$$

Pulling Out of a Dive, the Pilot of an Airplane