A civil engineer wishes to redesign the curved roadway in such a way that a car

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A civil engineer wishes to redesign the curved roadway in such a way that a car will not have to rely on friction to round the curve without skidding. In other words, a car moving at the designated speed can negotiate the curve even when the road is covered with ice. Such a ramp is usually banked, which means that the roadway is tilted toward the inside of the curve. Suppose the designated speed for the ramp is to be 10.0 m/s and the radius of the curve is 20.0 m. At what angle should the curve be banked?

Options:

A . 30∘

B . tan−113

C . 60∘

D . tan−112

Answer: Option D
:
D

A Civil Engineer Wishes To Redesign The Curved Roadway In Su...

\sum F_{r} = N s i n θ = \frac{m v^{2}}{r}

\sum F_{g} = N c o s θ - m g = 0

\Rightarrow t a n θ = \frac{v^{2}}{r g}

\Rightarrow θ = t a n^{- 1} (\frac{10^{2}}{(20) (10)}) = t a n^{- 1} (\frac{1}{2})

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