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(B) Given, $v_1 = 14 \ m/s$ and $v_2 = 28 \ m/s$. For a banked road, the angle of banking $	heta$ is related to the velocity $v$ and radius $r$ by th

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increase the radius by a factor of $4$

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(B) Given, $v_1 = 14 \ m/s$ and $v_2 = 28 \ m/s$. For a banked road, the angle of banking $	heta$ is related to the velocity $v$ and radius $r$ by the formula: $	an 	heta = \frac{v^2}{rg}$. Rearranging for radius, we get $r = \frac{v^2}{g 	an 	heta}$. Since the ramp is similar, the banking angle $	heta$ remains constant. Thus, $r \propto v^2$. Therefore, $\frac{r_2}{r_1} = \left( \frac{v_2}{v_1} ight)^2 = \left( \frac{28}{14} ight)^2 = (2)^2 = 4$. This implies $r_2 = 4r_1$. Hence, the radius should be increased by a factor of $4$.

$A$ circular freeway entrance and exit are commonly banked to control a moving car at $14 \ m/s$. To design a similar ramp for $28 \ m/s$, one should:

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