question_answer

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

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

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

C) Height of the table is 0.8 m

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

Correct Answer: A , C

Solution :

(a,c) Vertical component of velocity of ball at point P

\[{{v}_{V}}=0+gt=10\times 0.4=4\,m/s\]

Horizontal component of velocity = initial velocity

\[\Rightarrow {{v}_{H}}=4\,m/s\]

So the speed with which it hits the ground

\[v=\sqrt{v_{H}^{2}+v_{V}^{2}}=4\sqrt{2}\,m/s\]

and \[\tan \theta =\frac{{{v}_{V}}}{{{v}_{H}}}=\frac{4}{4}=1\] \[\Rightarrow \] \[\theta =45{}^\circ \]

It means the ball hits the ground at an angle of \[45{}^\circ \] to the horizontal.

Height of the table

\[h=\frac{1}{2}g{{t}^{2}}=\frac{1}{2}\times 10\times {{(0.4)}^{2}}=0.8\,m\]

Horizontal distance travelled by the ball from the edge of table \[h=ut=4\times 0.4=1.6\,m\]

Solution :

Same us above