question_answer

y component of velocity is 20 and x component of velocity is 10. The direction of motion of the body with the horizontal at this instant is                                 [Manipal 2003]

A)                 \[{{\tan }^{-1}}(2)\]

B)                             \[{{\tan }^{-1}}(1/2)\]

C)                 45°         

D)                 0°

Correct Answer: A

Solution :

                    \[{{v}_{y}}=20\] and \[{{v}_{x}}=10\]                                 \[\therefore \] velocity \[\vec{v}=10\hat{i}+20\hat{j}\]                                 direction of velocity with x axis                                 \[\tan \theta =\frac{{{v}_{y}}}{{{v}_{x}}}=\frac{20}{10}=2\]                 \[\therefore \] \[\theta ={{\tan }^{-1}}(2)\]