A) \[{{\mathbf{v}}_{0}}\]is \[8\hat{j}+4\hat{k}\]
B) position vector of location where two particles collide is \[16\hat{i}+32\hat{k}\]
C) Both [a] and [b] are correct
D) it is not possible that 8 and C collide with each other for any value of\[{{\mathbf{v}}_{0}}\]
Correct Answer: A
Solution :
Idea This question is based on motion. Here, one must know the resolution of vectors and about unit vectors. \[{{\mathbf{v}}_{A}}=3\hat{i}\] \[{{\mathbf{v}}_{B}}=8\hat{i}+2t\mathbf{\hat{k}}\], where Vg is velocity of B at any time t. Location of B at any time t is given by, \[{{\mathbf{r}}_{B}}=(8t)\mathbf{\hat{j}}+\frac{1}{2}(2{{t}^{2}})\mathbf{\hat{k}}\] Location of C at any time is given by, \[{{\mathbf{r}}_{C}}={{\mathbf{v}}_{0}}\times t\] So, from given condition, \[{{\mathbf{r}}_{B}}(t=4)={{r}_{C}}(t=4)\] \[\Rightarrow \]\[(8\times 4)\hat{j}+{{4}^{2}}\mathbf{\hat{k}}={{\mathbf{v}}_{0}}\times 4\] or \[{{\mathbf{v}}_{0}}=(8\hat{j}+4\mathbf{\hat{k}})m/s\] TEST Edge From this lesson questions on relative velocity in 2D could be asked. The river man problems could also be asked.
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