A spacecraft already experiences a force directed along due to the solar wind

PHYSICS · Single correct · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

A 1.2 × 103 kg1.2\,\times\,10^{3}\,\text{kg} spacecraft already experiences a 1.8 kN1.8\,\text{kN} force directed along +x+x due to the solar wind. Its main engine can provide thrusts up to 20 kN20\,\text{kN} in any direction. Mission control requires the craft to accelerate at 15 m/s215\,\text{m/s}^{2} in a direction 30∘30^\circ above the +x+x axis (in the xy-plane). Which of the following best states the additional engine thrust magnitude needed and whether the requirement is within the engine’s capability? (a) 20 kN20\,\text{kN}; requirement is just at the limit (b) 17 kN17\,\text{kN}; requirement is achievable (c) 16 kN16\,\text{kN}; requirement is achievable (d) 18 kN18\,\text{kN}; requirement is achievable

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