The motion of a 1.0-kg cart attached to a spring is describe…

The motion of a 1.0-kg cart attached to a spring is described by x(t)=(0.2 m)sin⁡[(π s−1)t]{“version”:”1.1″,”math”:”x(t) = (0.2 \text{ m})\sin{[(\pi \text{ s}^{-1})t]}”}a. What is the spring constant, k{“version”:”1.1″,”math”:”k”}?  (2 marks) b. What is the maximum speed, vmax{“version”:”1.1″,”math”:”vmax”}, of the cart?  (2 marks) c. What is the total energy of the system?  (3 marks) d. What is the maximum acceleration, amax{“version”:”1.1″,”math”:”amax”}, of the cart?  (3 marks)

Water is poured into a cylindrical container (radius R=5.00{…

Water is poured into a cylindrical container (radius R=5.00{“version”:”1.1″,”math”:”R=5.00″} cm) to a height h=20.0{“version”:”1.1″,”math”:”h=20.0″} cm. The container rests on the edge of a table a height H=1.00{“version”:”1.1″,”math”:”H=1.00″} m above the ground. If a small hole of radius r=1.50{“version”:”1.1″,”math”:”r=1.50″} mm is made in the container at h/4{“version”:”1.1″,”math”:”h/4″} from the bottom, how far does the water travel from the edge of the table before hitting the ground? (10 marks)