Question
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 $$\left( {\sqrt 3 m,1m} \right).$$ The value of $$\theta $$ is (gravitational effect is to be ignored)
A.
$${30^ \circ }$$
B.
$${60^ \circ }$$
C.
$${90^ \circ }$$
D.
$${120^ \circ }$$
Answer :
$${30^ \circ }$$
Solution :
From figure,
$$\tan \theta = \frac{{\sqrt 3 }}{1} = \sqrt 3 \Rightarrow \theta = {30^ \circ }$$
From figure,
$$\tan \theta = \frac{{\sqrt 3 }}{1} = \sqrt 3 \Rightarrow \theta = {30^ \circ }$$
