Question

In a vertical dive, a peregrine falcon can accelerate at 0.6 times the free-fall acceleration g (that is, at 0.6 g ) in reaching a speed of about 108 m / s. If a falcon pulls out of a dive into a circular arc at this speed and can sustain a radial acceleration of 0.6 g , what is the radius R of the turn?

Answer 1

The radius R of the turn is 1.984 km.

Explanation:

As the falcon is experiencing a centripetal motion, the acceleration exhibited by the falcon will be centripetal acceleration. The formula for centripetal acceleration is

                 $a=\frac{v^{2} }{R}$

Here a is the acceleration for centripetal motion, v is the velocity and R is the radius of the circular path.

As the centripetal acceleration is given as 0.6 g, the velocity is given as 108 m/s, then the radius of the path can be determined as

       $0.6 \times 9.8=\frac{(108)^{2}}{R}$

      $R=\frac{(108)^{2}}{0.6 \times 9.8}=\frac{11664}{5.88}=1983.67\ \mathrm{m}$

So, the radius of the turn is 1.984 km.