Question

A toy airplane is flying in a horizontal circular path. Its bank angle relative to the horizontal is estimated to be 35 degrees and the airplane takes 15 seconds to complete one circle. What is the radius of the airplanes’ circular path?

Answer 1

here,

theta = 35 degree

let the radius of the path be R

the speed of plane , v = 2 *pi * R /T

v = 2*pi*r /15 ....(1)

equating the forces vertically

N * cos(theta) = m * g ....(1)

and

N * sin(theta) = m * v^2 /r .....(2)

from (1) and (2)

tan(theta) = v^2 /(rg)

tan(45) = (2*pi*r/15 )^2 /(r * 9.81 )

solving for r

r = 55.9 m

the radius of track is 55.9 m