A small drone of mass is hovering when three independent thrusters fire simultaneously

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

A small drone of mass 1.8 kg1.8\,\text{kg} is hovering when three independent thrusters fire simultaneously, producing the following constant forces (expressed in unit-vector notation): F1=(2.5 i^+1.0 j^+0.0 k^) N\mathbf F_{1}=\bigl(2.5\,\mathbf{\hat i}+1.0\,\mathbf{\hat j}+0.0\,\mathbf{\hat k}\bigr)\,\text N, F2=(−1.0 i^+3.0 j^+2.0 k^) N\mathbf F_{2}=\bigl(-1.0\,\mathbf{\hat i}+3.0\,\mathbf{\hat j}+2.0\,\mathbf{\hat k}\bigr)\,\text N, F3=(0.0 i^−2.5 j^+1.5 k^) N\mathbf F_{3}=\bigl(0.0\,\mathbf{\hat i}-2.5\,\mathbf{\hat j}+1.5\,\mathbf{\hat k}\bigr)\,\text N. The i^\mathbf{\hat i}, j^\mathbf{\hat j}, and k^\mathbf{\hat k} unit vectors point in the +x+x (east), +y+y (north), and +z+z (upward) directions, respectively. Neglect air resistance. (a) Determine the Cartesian components of the net external force acting on the drone. (b) Calculate the Cartesian components of the drone’s acceleration. (c) Find the magnitude of the acceleration and the angle it makes above the horizontal plane. (d) If the magnitude of F3\mathbf F_{3} were doubled while the other forces remained unchanged, state qualitatively how each component of the acceleration would change.

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