Question

What is the radius of a bobsled turn banked at 75.0^\circ75.0 ​∘ ​​ and taken at 30.0 m/s, assuming it is ideally banked?

Answer 1

Banking angle is the angle between the normal horizontal path (N) and the curved banked path. The angle of banking of a curved path is defined as the angle through which the outer edge of the road is raised over the inner edge.

It is calculated as:

$tan\theta = \frac{v^2}{rg}$

Here,

v = Linear velocity of object

r = Radius of the curved path

$a_c$ = Acceleration due to gravity

Rewriting the equation to solve for the radius we have that

$r=\frac{v^2}{gtan\theta}$

$r = \frac{30}{(9.8)(tan 75\°)}$

$r = 24.6m$

Therefore the radius of a bobsled turn banked at 75° taken at 30m/s is 24.6m