• # question_answer At $t=0$, three particles A, Band Care located at the origin of the coordinate system. Then they start moving simultaneously, A moves with a constant velocity of 3i (m/s) and B moves under a constant acceleration of 2k (m/s2) with an initial velocity of 8j (m/s). Particle C moves with constant velocity v0 in such a way that B and C collide at t =4s. Then, A)  v0 is 8j + 4k B)  position vector of location where two particles collide is 16i + 32k C)  Both [a] and [b] are correct D)  it is not possible that B and C collide with each other for any value of v0

${{v}_{A}}=3i$ ${{v}_{B}}=8j+2t\,k,$ where Vg is velocity of B at any time t. Location of B at any time t is given by, ${{r}_{B}}=(8t)j+\frac{1}{2}\,(2{{t}^{2}})k$ Location of Cat any time ris given by. ${{r}_{C}}={{v}_{0}}\times t$ So, from given condition, ${{r}_{B}}\,(t=4)\,={{r}_{C}}\,(t=4)$ $\Rightarrow$            $(8\times 4)j+{{4}^{2}}k={{v}_{0}}\times 4$ or         ${{v}_{0}}=(8j+4k)\,m/s$