If we neglect air resistance, then the range of a ball (or any projectile) shot at an angle θ with respect to the x axis and with an initial velocity v0, is given by r(θ)= v02 g sin(2θ) for 0 ≤ θ ≤ π 2 where g is the acceleration due to gravity (9.8 meters per second per second). for what value of θ is the maximum range attained? (note that the answer is numerical, not symbolic.)

Atwo-stage air compressor operates at steady state, compression 10m^3/min of air from 100 kpa and 300k to 1200 kpa. an intercooler between the two stages cools the air to 300k at a constant pressure of 350 kpa. the compression processes are isentropic. a) calculate the power required to run the compressor, in kw b) compare the result to the power required for isentropic compression from the same inlet state to the same final pressure.