A roller coaster reaches the top of the steepest hill with a speed of 6.0 km/h. It then descends the hill, which is at an average angle of 45° and is 45.0 m long. What will its speed be when it reaches the bottom? Assume µk = 0.12.

A piece of ice (m = 1 Kg) slides down the slope of a roof inclined at 50.0°. It starts from rest and slides 8.0 m along the roof, sliding off the edge at a height of 4.0 m above the level ground. The coefficient of kinetic friction is 0.14. V¡ = 0.0 m/s m = 500.0 g 8,0 m Hx = 0.14 30° 4.0 m (a) Draw a free-body diagram of the ice as it is sliding along the roof. (b) Calculate the acceleration of the object. (c)With what speed does it leave the roof?

A small block slides down a frictionless track whose shape is described by y = (x^2) /d for x<0 and by y = -(x^2)/d for x>0. The value of d = 4.15m, and x and y are measured in meters as usual.  Now suppose the blocks starts on the track at x = 3.35 m. The block is given a push to the left and begins to slide up the track, eventually reaching its maximum height at x = 0, at which point it turns around and begins sliding down. What was its initial speed in this case?     4.05 m/s     7.28 m/s     5.15 m/s     4.97 m/s

The figure below shows a motorcycle leaving the end of a ramp with a speed of 39.6 m/s and following the curved path shown. At the peak of the path, a maximum height h above the top of the ramp, the motorcycle's speed is 37.7 m/s. What is the maximum height h? Ignore friction and air resistance. (Enter your answer in m.)