A roller coaster is designed such that riders | vedclass

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(A) At the top of the hill, the forces acting on the rider are the gravitational force $Mg$ (downwards) and the normal reaction $N$ (upwards).The net

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$14 \, m/s$ and $15 \, m/s$

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(A) At the top of the hill, the forces acting on the rider are the gravitational force $Mg$ (downwards) and the normal reaction $N$ (upwards).The net centripetal force is provided by the difference between these forces:$Mg - N = M \frac{v^2}{R}$For the condition of "weightlessness", the normal reaction $N$ must be zero $(N = 0)$.Substituting $N = 0$ into the equation:$Mg = M \frac{v^2}{R}$$g = \frac{v^2}{R}$$v = \sqrt{Rg}$Given $R = 20 \, m$ and taking $g = 10 \, m/s^2$:$v = \sqrt{20 	imes 10} = \sqrt{200} \approx 14.14 \, m/s$Therefore, the speed of the car at the top of the hill is between $14 \, m/s$ and $15 \, m/s$.

$A$ roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20 \, m$. The speed of the car at the top of the hill is between

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