Question

hi 5. The picture 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 hy = 4.36 m and over the first peak with height hz = 6.77 m above the lowest point on the track. The shape of the first peak is a circle with a radius of R = 5.97 m. The ride is designed so that the riders feel weightless at the top of the first hill, hz. "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?

Answer 1

At the top of first hill, hz Weight Contripetal force mu? R v² = mg R ag V Rg = 15.97*9.84 7.652 mls v Now From conservation of energy Final energy Initial energy ghi th. Vi ² → ngh, + 1 mvit = mghat I mive ghet ₂ ve > 9.81* 4:36 + 1 _ V = 9.81*6.77 → 42.7116 +1V== 95.69 mis Aron 2. tl *7.652 2 ŽV; ² V Vi = 52.918 10.287 = 105.837 swer