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 :

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