Project Gravita

Classical Mechanics Level 4

A particle is projected from the surface of the earth (of radius R and mass M) with speed \(V\) given by

\[V=\sqrt{\frac{GM}{R}}\] at a certain angle from the local horizantal as shown in the figure such that the angle subtended by arc between launching and landing site at earth's centre is \[\beta=\frac{\pi}{2}\]

Maximum separation of the particle from the centre of the earth is xR. find \( \lfloor 10x\rfloor \)

Consider the earth to be uniformly dense and air resistance to be absent.


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