Question

Ball, with mass m, released from rest at a height y,o- Air resistance is found to be FD-KV2. (a) Find the Eulerian description of this velocity field. (2006) (b) Find the acceleration for this velocity field. (20%) mg

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Answer 1

" Net Force acting on the Ball f_Nel = mg-kV^2 As we know f = ma = mV dV/dy mV dv/dy = mg-kV^2 mv dv/mg-kV^2 = dy put limit Both side at y = y_0 V = 0 at the point of drop at y = y V is velocity integral^V_0 mV dV/mg-kV^2 = integral^y_y_0 dy put mg-kv^2 = z some other variable Diffenciate both side -g kV dV = dz V dV = -dz/gk \r\n -1/2k integral mg-kV^2_mg m dz/z = integral^y_y_0 dy when V = 0 z = mg V = v z = mg-kV^2