Imagine a landing craft approaching the surface of the moon of a distant planet. if the engine provides an upward force (thrust) of 3470 n, the craft descends at constant speed; if the engine provides only 2200 n, the craft accelerates downward at 0.37 m/s2.(a) what is the weight of the landing craft in the vicinity of callisto’s surface? (b) what is the mass of the craft? (c) what is the magnitude of the free-fall acceleration near the surface of callisto?

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.)

Question part points submissions used suppose that 2 j of work is needed to stretch a spring from its natural length of 26 cm to a length of 36 cm. (a) how much work is needed to stretch the spring from 28 cm to 32 cm? (round your answer to two decimal places.)

Atank has a shape of a cone with a radius at the top of 2 m and a height of 5 m. the tank also has a 1 m spout at the top of the tank. the tank is filled with water up to a height of 2 m. find the work needed to pump all the water out the top of the spout. (use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.)