A model spacecraft in deep space is initially moving with velocity

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum

Problem

A 250 g250\,\text{g} model spacecraft in deep space is initially moving with velocity v0=(12 i^+5 j^) m s−1\mathbf v_0 = (12\,\hat{i} + 5\,\hat{j})\,\text{m\,s}^{-1}. It fires three short attitude-control jets in succession. • Jet 1 acts for 0.20 s0.20\,\text{s} and gives the craft a velocity change Δv1=(−3 i^+4 j^) m s−1\Delta\mathbf v_1 = (-3\,\hat{i} + 4\,\hat{j})\,\text{m\,s}^{-1}. • Jet 2 acts for 0.15 s0.15\,\text{s} and produces Δv2=(6 i^−2 j^) m s−1\Delta\mathbf v_2 = (6\,\hat{i} - 2\,\hat{j})\,\text{m\,s}^{-1}. • Jet 3 acts for 0.10 s0.10\,\text{s} and produces Δv3=(−2 i^−3 j^) m s−1\Delta\mathbf v_3 = (-2\,\hat{i} - 3\,\hat{j})\,\text{m\,s}^{-1}. (i) For each jet, calculate the corresponding change in momentum of the spacecraft. (ii) Determine the net change in momentum after all three jets have fired and hence write the final velocity vector of the spacecraft. (iii) Compute the magnitude of the average resultant force acting on the spacecraft during the entire 0.45 s0.45\,\text{s} firing sequence.

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