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.

Step-by-step 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=(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 * 9.8=((108)^(2))/(R)`

`R=((108)^(2))/(0.6 * 9.8)=(11664)/(5.88)=1983.67\ \mathrm{m}`

So, the radius of the turn is 1.984 km.