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Recall that we had discussed relative velocity in the previous module. The equation for relative velocity was \(v_{AB} = v_{AC} + v_{CB}\). This can be made a vector equation, \(\vec{v}_{AB} = \vec{v}_{AC} + \vec{v}_{CB}\). Similarly, recall that \(v_{AB} = -v_{BA}\)
An aeroplane is flying Eastwards at \(1000 \, \mathrm{km/h}\) wrt the wind. The wind is blowing due North at \(50 \, \mathrm{km/h}\) wrt the ground. What is the velocity of the aeroplane wrt the ground? (Hint: Use A instead of Aeroplane, B instead of Ground, C instead of Wind. We are looking for \(v_{\text{Aeroplane}\, \text{Ground}}\))
  • \(1000 \hat{i} - 50 \hat{j}\)
  • \(1000 \hat{i} + 50 \hat{j}\)
  • \(1050 \hat{i} + 1050 \hat{j}\)
  • \(1050 \hat{i} - 1050 \hat{j}\)