Question

The picture above shows the launch and first hills of a roller coaster. The cars are...

The picture above shows the launch and first hills of a roller coaster. The cars are launched with some initial velocity, vi, go down a hill of height h1 = 4.13 m and over the first peak with height h2 = 7.69 m above the lowest point on the track.

The shape of the first peak is a circle with a radius of R = 5.01 m.

The ride is designed so that the riders feel weightless at the top of the first hill, h2. "Weightless" means that the rider feels like he or she is in free fall.

What is the initial velocity vi that is needed to give the riders the feeling of weightlessness?

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