A baseball with a mass of m = 0.19 kg is pushed down onto the top of a vertical spring compressing the spring a distance of d = 0.16 meters spring constant of the spring is k = 650 N/m gravitational potential energy is 0 What is the ball’s velocity at half of the maximum height relative to the equilibrium point?

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.)

Two forces produce equal torques on a door about the door hinge. the first force is applied at the midpoint of the door; the second force is applied at the doorknob. both forces are applied perpendicular to the door. which force has a greater magnitude?

Aforce of 100 newtons is used to move an object a distance of 15 meters with a power of 50 watts. find the work dine and the time it takes to do the work