An engineer wants to design an oval racetrack such that 1.424 x 104 N race cars can round the exactly 304.9 m radius turns at 45.6 m/s without the aid of friction. She estimates that the cars will round the turns at a maximum of 78.2 m/s. Find the banking angle θ necessary for the race cars to navigate the turns at 45.6 m/s without the aid of friction.

The banking angle required is .

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 =(rg ÷ tanθ)

where: r is the radius of the road, g is the gravitational force and θ is the banking angle.

⇒ = rg ÷ tanθ

   tanθ =

     θ    =    

           =     (given that g = 10)

           =

          = 1.4663

     θ   =

The banking angle required is .

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

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