The car shall not be successful since the corner must have a radius as nine times as the real corner designed for a suggested speed of 15 miles per hour.
By definition of centripetal acceleration, the square of the velocity taken by the vehicle ([tex]v[/tex]), in miles per hour, is directly proportional to the radius of the corner ([tex]R[/tex]), in meters. Then, we have the following relationship:
[tex]\frac{v_{A}^{2}}{R_{A}} = \frac{v_{B}^{2}}{R_{B}}[/tex] (1)
Where:
If we know that [tex]v_{A} = 15\,\frac{mi}{h}[/tex], [tex]v_{B} = 45\,\frac{mi}{h}[/tex] and [tex]R_{A} = k[/tex], then the expected radius of the corner is:
[tex]R_{B} = k\cdot \left(\frac{v_{B}}{v_{A}} \right)^{2}[/tex]
[tex]R_{B} = 9\cdot k[/tex]
In order to successfully take a corner at 45 miles per hour, the corner must have a radius as nine times as the real corner designed for a suggested speed of 15 miles per hour. Thus, the car shall not be successful at a speed of 45 miles per hour.
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