question_answer

A boat is moving with a velocity \[(\text{3\hat{i}}+\text{4\hat{j}})\] with respect to ground. The water in the river is moving with a velocity \[-\text{3\hat{i}}-\text{4\hat{j}}\] with respect to ground. What is the relative velocity of boat with respect to water?                

Answer:

Velocity of boat w.r.t. ground\[{{\vec{v}}_{B}}=\text{3\hat{i}}+\text{4\hat{j}}\];. Velocity of water w.r.t. ground\[{{\vec{v}}_{W}}=-\text{3\hat{i}}-\text{4\hat{j}}\]. Relative velocity of boat w.r.t. water is \[{{\vec{v}}_{BW}}={{\vec{v}}_{B}}-{{\vec{v}}_{W}}=\left( \text{3\hat{i}}+\text{4\hat{j}} \right)\left( -\text{3\hat{i}}-\text{4\hat{j}} \right)=\text{6\hat{i}}+\text{8\hat{j}}\]