The Lunar Module could make a safe landing if its vertical velocity at impact is 3.0 m/s or less. Suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is (a) zero; (b) 2.0 m/s downward; (c) 2.0 m/s upward. Use conservation of energy to determine h in each case. The acceleration due to gravity at the surface of the Moon is 1.62 m/s2.

Consider a one meter long horizontal pipe with a constant 100 cm^2 cross sectional area. water flows rightward into the pipe at x = 0 with flow velocity 02m/sec at every point within the pipe intake area. at x=1, the rightward flow rate is 0.192 m/sec. assume the water is a conserved quantity in the pipe, so there must be a leak (a sink) somewhere in the pipe. 1. compute net volumetric flow of the source if the system to be in equilibrium. 2. now assume the pipe in the problem has no leaks. compute the net volumetric rate of change for the system.