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# $v_A=(x \hat i+6 \hat j) m/s,v_B=(3 \hat i+2 \hat j) m/s$ find x such that the relative speed of A with respect to B becomes 5 m/s

$(a)\; 3 \quad (b)\;4 \quad (c)\;5 \quad (d)6$

$v_{AB}=v_A-v_B$
$\qquad=(x-3) \hat i+(6-2) \hat j$
$\qquad= (x-3) \hat i+4 \hat j$
Speed$=|\bar {v}_{AB}|$
$\qquad=5$
$\qquad=\sqrt {(x-3)^2+4^2}$
$\qquad=>25=(x-3)^2+16$
$\qquad=>x=6\; or \;0$
Hence d is the correct answer.

edited Jan 25, 2014 by meena.p