Question

A jet is flying at 134.1 m/s along a straight line and makes a turn along a circular path level with the ground. What does the radius of the circle have to be to produce a centripetal acceleration of 1 g on the pilot and jet toward the center of the circular trajectory?

Answer 1

Given:

A jet is flying at 134.1 m/s along a straight line and makes a turn along a circular path level with the ground.

To find:

Radius of circle for the pilot to experience 1g centripetal acceleration?

Calculation:

The general expression for centripetal force is:

$F = \dfrac{m {v}^{2} }{r}$

$\implies \dfrac{F}{m} = \dfrac{ {v}^{2} }{r}$

$\implies a_{c}= \dfrac{ {v}^{2} }{r}$

$\implies 1g= \dfrac{ {(134.1)}^{2} }{r}$

$\implies 9.8= \dfrac{ {(134.1)}^{2} }{r}$

$\implies r= \dfrac{ {(134.1)}^{2} }{9.8}$

$\implies r= 1834.9 \: m$

$\implies r= 1.83 \: km$

So, the radius of circle is 1.83 km.