question_answer

A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of\[2\text{ }m/s\]. At what angle \[\alpha \] with the vertical should the screen be placed so that the rain drops falling downwards with velocity \[6m/s\]strike the windscreen perpendicularly?

A) \[{{\tan }^{-1}}(1/3)\]              

B) \[{{\tan }^{-1}}(3)\]         

C)     \[{{\cos }^{-1}}(3)\]              

D)       \[si{{n}^{-1}}(1/3)\]

Correct Answer: B

Solution :

[b] Velocity of rain with respect to car\[\overset{\to }{\mathop{{{v}_{RC}}}}\,={{\overset{\to }{\mathop{v}}\,}_{RC}}-\overset{\to }{\mathop{{{C}_{C}}}}\,\]  should be perpendicular to the wind screen. i.e., components of \[\overset{\to }{\mathop{{{v}_{R}}}}\,\] and \[-{{\overset{\to }{\mathop{v}}\,}_{C}}\] parallel to wind screen should be zero. or         \[6\cos \alpha =2\sin \alpha \] or         \[\tan \alpha =3\] or         \[\alpha ={{\tan }^{-1}}(3)\]