question_answer

A ball is rolled off the edge of a horizontal table at a speed of 4 m/s. It hits the ground after 0.4 sec. Which statement given below is true?

A) It hits the ground at a horizontal distance 1.6m from the edge of the table

B) The speed with which it hits the ground is 4.0 m/s

C) Height of the table is 0.9 m  

D) It hits the ground at an angle of \[60{}^\circ \] to the horizontal

Correct Answer: A

Solution :

\[\therefore \,\,\,R=u.T=4\times 0.4=1.6\,m\] \[{{V}_{y}}=gT=4\text{ }m/s\]   \[\therefore \,\,\text{ }v=\,\,{{\sqrt{{{v}^{2}}_{x}+{{v}^{2}}}}_{y}}=4\sqrt{2}\text{ }m/s\]\[H=\frac{1}{2}\,\,g{{T}^{2}}\,\,=\,\frac{1}{2}\times 10\times {{(0.4)}^{2}}\,\,=\,\,0.8\,m\] \[~tan\text{ }\alpha =\,\,\frac{{{v}_{y}}}{{{v}_{x}}}=1\,\,\,\Rightarrow \text{ }\alpha =45{}^\circ \]