An empty cylindrical barrel is open at one end and rolls without slipping straight down a hill. The barrel has a mass of 15.0 kg, a radius of 0.400 m, and a length of 0.800 m. The mass of the end of the barrel equals a fourth of the mass of its side, and the thickness of the barrel is negligible. The acceleration due to gravity is =9.80 m/s2. What is the translational speed f of the barrel at the bottom of the hill if released from rest at a height of 33.0 m above the bottom?

Abasketball star covers 2.65 m horizontally in a jump to dunk the ball. his motion through space can be modeled precisely as that of a particle at his center of mass. his center of mass is at elevation 1.02 m when he leaves the floor. it reaches a maximum height of 1.90 m above the floor and is at elevation 0.910 m when he touches down again. (a) determine his time of flight (his "hang time"). (b) determine his horizontal velocity at the instant of takeoff. (c) determine his vertical velocity at the instant of takeoff. (d) determine his takeoff angle. (e) for comparison, determine the hang time of a whitetail deer making a jump with center-of-mass elevations yi = 1.20 m, ymax = 2.45 m, and yf = 0.750 m.