The specifications for the ascent stage of a lunar module include the following: All-up mass on take-off = 5000 kg. Specific impulse Isp= 350 s. Thrust-to-weight ratio at take-off = 6.0. Take-off direction: vertical. Thrust profile: constant, at take-off setting. (a) Acceleration due to gravity close to the Lunar and Earth surfaces is 1.62 m s and 9.81 m sz, respectively. (b) Calculate the vertical velocity V, achieved after the first twenty seconds of vertical flight from the lunar surface. Estimate the altitude gain. After twenty seconds of vertical flight, the vehicle is rapidly pitched through twenty degrees, and its new attitude maintained constant thereafter by an automatic control system. Estimate the vehicle's velocity vector and speed after a further one hundred and twenty seconds of powered flight.