Aparticle m is thrown vertically upward with an initial velocity v. assuming a resisting medium proportional to the velocity, where the proportionality factor is c, calculate the velocity with which the particle will strike the ground upon its return if there is a uniform gravitational field.

Ten students stand in a circle and are told to make a transverse wave. what best describes the motion of the students? each student bumps the shoulder of his or her neighbor. at the exact time, all students take a step to the right. the students skip clockwise, going in a circular motion. one at a time, each student lifts his or her hands up and then down.

Identify the forces that contribute to the centripetal force on the object in each of the following examples: a. a bicyclist moving around a flat, circular track b. a bicycle moving around a flat, circular track c. a racecar turning a corner on a steeply banked curve

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.)