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Question

Two identical smooth balls are projected from points O and A on the horizontal ground with same speed of projection. the angle of projection in each case is 30$$^o$$ (see figure). The distance between O and A is 100 m. The balls collide in mid-air and return to their respective points of projection. If the coefficient of restitution is 0.7, find the speed of projection of either ball (in m/s) correct to nearest integer. (Take $$g = 10  m s^{-2}$$ and $$\sqrt{3} = 1.7$$)
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Solution

Total time of flight of one object is $$t=\dfrac { 24\sin { \theta  }  }{ g } $$
$$=\dfrac { 24\sin { 30° }  }{ g } =\dfrac { 4 }{ g } $$
In this period both object travel 100m horizontal distance 50 m with speed $$4\cos 30°$$ where e = coefficient of resistution 
Now $$t=\dfrac { 50 }{ u\cos { 30° }  } +\dfrac { 50 }{ eu\cos { 30° }  } $$
$$ \dfrac { u }{ g } =\dfrac { 50 }{ 4\times \sqrt { \dfrac { 3 }{ 2 }  }  } +\dfrac { 50 }{ 0.7\times \sqrt { \dfrac { 3 }{ 2 }  } 4 } \\ { u }^{ 2 }=g\left( 100\left( \dfrac { 1 }{ \sqrt { 3 }  } +\dfrac { 1 }{ 0.7\times \sqrt { 3 }  }  \right)  \right) \\ =100g\times 1.428\\ { u }^{ 2 }=1428=(37.8)^{ 2 }\\ u\approx 38.m/s$$

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Physics

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