Answer:
The banking angle required is [tex]55.7^{0}[/tex].
Explanation:
Banking of a road is the act of constructing a road along a curved path at a certain angle to avoid skidding-off of vehicles plying it. Centripetal force is required to pull the object moving with a velocity 'v' towards the center of the curve for stability.
The velocity of a car navigating a banked road is given by:
v =[tex]\sqrt{ }[/tex](rg ÷ tanθ)
where: r is the radius of the road, g is the gravitational force and θ is the banking angle.
⇒ [tex]v^{2}[/tex] = rg ÷ tanθ
tanθ = [tex]\frac{rg}{v^{2} }[/tex]
θ = [tex]tan^{-1}[/tex] [tex]\frac{rg}{v^{2} }[/tex]
= [tex]tan^{-1}[/tex] [tex]\frac{304.9 * 10}{45.6^{2} }[/tex] (given that g = 10[tex]ms^{-2}[/tex])
= [tex]tan^{-1}[/tex] [tex]\frac{3049}{2079.36}[/tex]
= [tex]tan^{-1}[/tex] 1.4663
θ = [tex]55.7^{0}[/tex]
The banking angle required is [tex]55.7^{0}[/tex].
