JEE Main & Advanced Sample Paper JEE Main Sample Paper-45

  • 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

    Correct Answer: A

    Solution :

     \[{{v}_{A}}=3i\] \[{{v}_{B}}=8j+2t\,k,\] 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         \[{{v}_{0}}=(8j+4k)\,m/s\]

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