question_answer

A boy is standing on a cart moving along x-axis with the speed of 10 m/s. When the cart reaches the origin he throws a stone in the horizontal x-y plane with the speed of 5 m/s with respect to himself at an angle \[\theta \] with the x-axis. It is found that the stone hits a ball lying at rest at a point whose co-ordinates are\[\left( \sqrt{3}\,m,\text{ }1\,m \right)\]. The value of \[\theta \] is (gravitational effect is to be ignored)

A) \[30{}^\circ \]              

B)        \[60{}^\circ \]  

C) \[90{}^\circ \]              

D)        \[120{}^\circ \]

Correct Answer: A

Solution :

[a] From figure, \[\tan \theta =\frac{\sqrt{3}}{1}=\sqrt{3}\Rightarrow \theta =30{}^\circ \]