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Numerical problems related to physics, specifically involving the motion of a roller coaster and a skydiver. Students are required to calculate the force exerted on the roller coaster by the track, the maximum speed of the roller coaster at a certain point, the acceleration and drag forces on the skydiver at different speeds.
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Q. A roller coaster car has a mass of 500 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. (a) If the vehicle has a speed of 20.0 m/s at point A, what is the force exerted by the track on the car at this point? (b) What is the maximum speed the vehicle can have at point B and still remain on the track? Assume the roller-coaster tracks at points A and B are parts of vertical circles of radius r1 = 10.0 m and r2 = 15.0 m, respectively.
Q. A skydiver of mass 80.0 kg jumps from a slow-moving aircraft and reaches a terminal speed of 50.0 m/s.
(a) What is her acceleration when her speed is 30.0 m/s? What is the drag force on the skydiver when her speed is (b) 50.0 m/s and (c) 30.0 m/s?