A simple pendulum is swinging back and forth through a small angle, its motion repeating every 1.15 is. How much longer should the pendulum be made in order to increase its period by 0.22 s?

Imagine that someone pushes one marble toward a motionless marble. would there still be action-reaction forces involved in the collision? how might the marbles’ motions be changed? ?

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

Explain earth's motion, using the terms "precession" and "rotation" in your answer.