FYKOS Year 35 Series 6 Problem 5 — fly rocket, fly · FYKOS 35 #35.6.5

Physics · mechanics · optics

Problem

We have constructed a small rocket weighing m0=3 kgm_0 = 3\,\mathrm{kg}, from which 70%70\% is fuel. The exhaust velocity is u=200 m⋅s−1u = 200\,\mathrm{m\cdot s^{-1}} and the initial flow of the exhaust fumes is R=0.1 kg⋅s−1R = 0.1\,\mathrm{kg\cdot s^{-1}} and both these values remain constant during the flight. The rocket is equipped with stabilization elements, so it does not deviate from its desired trajectory. It has been launched from the rest position vertically. Assume that the friction force of the air is proportional to the velocity Fo=−bvF_{\mathrm{o}} = -bv, where b=0.05 kg⋅s−1b = 0.05\,\mathrm{kg\cdot s^{-1}}, vv is the velocity of the rocket and the sign minus means that the force exerts against the direction of the motion. What height above the ground level does the rocket fly in time T=25 sT = 25\,\mathrm{s} from the engine startup?

Related theory

Browse the problem library