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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

Options

  1. A14 ~m / s and 15 ~m / s
  2. B15 ~m / s and 16 ~m / s
  3. C16 ~m / s and 17 ~m / s
  4. D13 ~m / s and 14 ~m / s

Correct answer

A. 14 ~m / s and 15 ~m / s

Step-by-step solution

Balancing the forces, we get M g-N=M v² R For weightlessness, N=0 M v² R =M g where R is the radius of curvature and v is the speed of car. Therefore, v= Rg Putting the values, R=20 ~m , g=10.0 ~m / s ² So, v= 20 10.0 =14.14 ~m / s ² Thus, the speed of the car at the top of the hill is between 14 ~m / s and 15 ~m / s . Note : The roller coaster is a popular amusement ride developed for amusement parks and modern theme parks.

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