A parachutist whose mass is 80 kg drops from a helicopter hovering 1000 m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the parachutist, with the proportionality constant b, 30 N-sec/m when the chute is closed and by 100 N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 20 m/sec, after how many seconds will the parachutist reach the ground? Assume that the acceleration due to gravity is 9.81 m/sec. The parachutist will reach the ground after 2.01 seconds.

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The motion of a train of mass 340M8 is opposed by a tractive resistance to motion of 190N/Mg. The train covers a total distance of 800m while accelerating during 1.5min on its way up an incline of 1 in 140 from an initial speed of 18km/h Analyse the motion and calculate: • The magnitude of the tractive resistance to motion in N: N • The speed of the train after 1.5min up the incline, m/s The acceleration of the train, a = m/s? • The force delivered from the train engine to achieve the acceleration, Fdr = • The power output at the instant the train reaches 800m, P = W Assume the power is witched off immediately after the train has reached 800m, analyze the further part of the motions and calculate: • how long, after the initial 1.5 min will the train still move up the incline before stopping, assuming the same tractive resistance to motions with no brakes applied, At = • Calculate the variation of the potential and kinetic energies between the initial instant at 18 km/h and the moment…

A helicopter with a mass of 10,000 kg takes off straight up at t=0. The thrust of the engine is defined given as a function of time: FT= 95 0.18t- (kN). Where t is in units of seconds. How fast is it rising and what is its elevation at t=4s?