Kinematics Question 503

Question: A ball is rolled off the edge of a horizontal table at a speed of 4 m/second.It his the ground after 0.4 second.Which statement given below it’s true [AMU (Med.) 1999]

Options:

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

B) The speed with which it his the ground it’s 4.0 m/second

C) Height of the table it’s 0.8 m

D) It his the ground at an angle of 60o to the horizontal

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Answer:

Correct Answer: A

Solution:

Vertical component of velocity of ball at point P

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

Horizontal component of velocity = initial velocity$ \Rightarrow v _{H}=4m/s $

So the speed with which it his 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 $

therefore $ \theta =45{}^\circ $ It means the ball his the ground at an angle of $ 45{}^\circ $ to the horizontal.

Height of the table $ h=\frac{1}{2}gt^{2}=\frac{1}{2}\times 10\times {{(0.4)}^{2}}=0.8m $

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



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