At the end of the Galactic Green Lion roller coaster, a 400 kg car has a speed of 22 m/s (point A). For safety, the coaster has to be going only 3 m/s when it enters the platform (point B) for the brakes to be able to stop in time. How high does the final hill need to be to slow down the coaster enough?

The space between two 15-in.-long concentric cylinders is filled with glycerin (viscosity = 8.5 × 10-3 lb·s/ft2). the inner cylinder has a radius of 1 in. and the gap width between cylinders is 0.1 in. determine (a) the torque and (b) the power required to rotate the inner cylinder at 180 rev/min. the outer cylinder is fixed. assume the velocity distribution in the gap to be linear.