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Compute the velocity of a free-falling parachutist using Euler's method for the case where m = 80 kg and c = 10 kg/s. Perform the calculation from t = 0 to 20 s with a step size of 1 s. Use an initial condition that the parachutist has an upward velocity of 20 m/s at t = 0. At t = 10 s, assume that the chute is instantaneously deployed so that the drag coefficient jumps to 50 kg/s

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Valentin Bogatu eNotes educator | Certified Educator

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The equation of motion is

`m*a = G - c*v`

`m*(dv)/dt = m*g -c*v`

where all quantities are positive downwards.

Taking `dt = Delta(t)= 1 s` and `dv = Delta(v) = v_(n+1) -v_n` we have

`v_(n+1) = v_n +[g -(c/m)*v_n]*Delta(t)`

Applying Euler method with the initial conditions `v_0 =-20 m/s` , `c =10 (kg)/s` we get

`v_1 =-20 +(9.8 + 10/80*20)*1 =-7.7 m/s`

`v_2 =-7.7 +(9.8+10/80*7.7)*1 = 3.06 m/s`

`v_3 =3.06...

(The entire section contains 158 words.)

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