An aircraft executes a horizontal loop of radius $1.00 ext{ km}$ with a steady speed of $900 ext{

Question

An aircraft executes a horizontal loop of radius $1.00	ext{ km}$ with a steady speed of $900	ext{ km/h}$. What is the ratio of its centripetal acceleration to the acceleration due to gravity? (Take $g = 9.8	ext{ m/s}^2$)

Professor PC Thomas Classes · Answer

Speed $v = 900	ext{ km/h} = 900 	imes \frac{5}{18} = 250	ext{ m/s}$. Radius $R = 1000	ext{ m}$. Centripetal acceleration $a_c = \frac{v^2}{R} = \frac{(250)^2}{1000} = 62.5	ext{ m/s}^2$. The ratio is $\frac{a_c}{g} = \frac{62.5}{9.8} \approx 6.38 \approx 6.4$.