)a 1.0 kilogram laboratory cart moving with a velocity of 0.50 meter per second due east collides with and sticks to a similar cart initially at rest. after the collision, the two carts move off together with a velocity of 0.25 meter per second due east. the total momentum of this frictionless system is

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.)

Arocket starts from rest and moves upward from the surface of the earth. for the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay = 12.80 m/s32t, where the +y-direction is upward. (a) what is the height of the rocket above the surface of the earth at t = 10.0 s? b) what is the speed of the rocket when it is 325 m above the surface of the earth?

Urgent pls a. coal consumption levels off and remains flat. b. petroleum, natural gas, and renewables show an increase in consumption c. more nonrenewable resources continued to be consumed than renewable. d. there is little projected increase in nuclear energy use. e. carbon dioxide emissions are projected to decline as we approach 2040. global energy consumption is defined as the total energy used by an individual or organizations from around the world. use the graph above to analyze the projected energy consumption from now until 2040. which statements in the prompt apply? a) a, b, d b) b, c, d c) a, c, d d) a, b, c, d