question_answer

Wind is blowing at constant velocity\[\text{\vec{V}}\]towards west. A man initially at rest start moving with constant acceleration \[a\] towards north. Then the moment of time at which direction of wind appears south west to him is

A) \[\frac{\left| \overset{\to }{\mathop{V}}\, \right|}{\left| \overset{\to }{\mathop{a}}\, \right|}\]                                           

B) \[\frac{\left| 2\overset{\to }{\mathop{V}}\, \right|}{\left| \overset{\to }{\mathop{a}}\, \right|}\]

C) \[\frac{\left| 3\overset{\to }{\mathop{V}}\, \right|}{\left| \overset{\to }{\mathop{a}}\, \right|}\]                                         

D)  none of these

Correct Answer: A

Solution :

\[{{\overset{\bullet }{\mathop{\text{V}}}\,}_{\text{Wind/Man}}}={{\overset{\to }{\mathop{\text{V}}}\,}_{\text{W}}}-{{\overset{\to }{\mathop{\text{V}}}\,}_{\text{M}}}\]\[|{{\overset{\to }{\mathop{\text{V}}}\,}_{\text{M}}}|=|{{\overset{\to }{\mathop{\text{V}}}\,}_{\text{W}}}|\] \[\text{V}=0+\]at\[t=\frac{|\overset{\to }{\mathop{\text{V}}}\,|}{|\overset{\to }{\mathop{\text{a}}}\,|}\]