Answer:
[tex]\theta=50.79^{\circ}[/tex]
Explanation:
The radius of curvature of the velodrome, r = 20 m
Speed of cyclists, v = 15.5 m/s
Let [tex]\theta[/tex] is the angle at which the surface should be banked. The horizontal and vertical forces acting on the cyclists are as follows :
[tex]F_x=\dfrac{mv^2}{r}[/tex]
[tex]F_y=mg[/tex]
From the above two equations,
[tex]tan\theta=\dfrac{v^2}{rg}[/tex]
[tex]tan\theta=\dfrac{(15.5)^2}{20\times 9.8}[/tex]
[tex]tan\theta=1.225[/tex]
[tex]\theta=50.79^{\circ}[/tex]
So, the angle at which the surface is banked is 50.79 degrees. Hence, this is the required solution.
