question_answer

A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u. The ratio of their velocities when they reach the earth's surface will be

A) \[\sqrt{2gh+{{u}^{2}}}\,\,:\,\,u\]          

B) \[1\,\,:\,\,2\]

C) \[1\,\,:\,\,1\]                               

D) \[\sqrt{2gh+{{u}^{2}}}\,\,:\,\,\sqrt{2gh}\]  

Correct Answer: C

Solution :

When particle is thrown in vertical downward direction with velocity u then final velocity at the ground level \[{{v}^{2}}={{u}^{2}}+2\,gh\,\,\,\,\,\,\,\,\therefore \,\,\,\,\,v=\sqrt{{{u}^{2}}+2gh}\]P" Another particle is thrown horizontally with same velocity then at the surface of earth. Horizontal component of velocity v^ = u \[\therefore \,\,\,\,\,Resultant\,\,velocity,\,\,\,\,v=\sqrt{{{u}^{2}}+2gh}\] For both the particles final velocities when they reach the earth?s surface are equal.