Answer to Question #199750 in Mechanics | Relativity for Surya

Question

An aerobatic aircraft is performing circular loops at the speed of sound, covering spectacularly 340 meters every single second in a flight exhibition. All participants have been warned that they keep their acceleration below 8 times that of the gravitational acceleration to avoid getting dizzy. What is the diameter of the smallest loop that these participants can safely do? Here you may use 10 m/s/s as the gravitational acceleration.

Answer 1

Solution.

$v=340m/s;$

$a=\dfrac{g}{8}m/s^2;$

$g=10m/s^2;$

$a=\dfrac{v^2}{r}\implies r=\dfrac{v^2}{a};$

$r=\dfrac{(340m/s)^2}{\dfrac{10}{8}m/s^2}=92480m;$

$d=2r=2\sdot 92480m=184960m;$

Answer: $d=184960m.$