A skyrocket firework burns fuel as it climbs. Its mass, m(h) kg, at height h m is given by (a) What is the mass of the rocket at h = 0 just before it is launched? (b) Show that the mass decreases as the rocket climbs. (c) Whatwork would be required to lift the rocket 10 m if its mass did not decrease? (d) Approximate the work done as the rocket goes from height h to h + Δh. (e) The rocket explodes at h = 250 m. Find total work done by the rocket from launch to explosion.

How is the gravitational force related to the distance between two objects?

Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.

Water is siphoned from a large tank and discharges into the atmosphere through a 50-mm diameter tube. the end of the tube is b = 2.1 m below the tank bottom which is a = 7.4 m deep, and viscous effects are negligible. determine the maximum height h over which the water can be siphoned without cavitation occurring. atmospheric pressure is 101.4 kpa, and the water vapor pressure is 1.79 kpa (absolute)