A particle is projected vertically upwards from the surface of the Earth with a velocity equal to half the escape velocity. What is the maximum height reached by the particle?

A. R/3 — Using conservation of energy, the initial kinetic plus potential energy equals the potential energy at maximum height. Solving for h gives R/3.

JEE Advanced · PhysicsMedium

$A particle is projected vertically upwards from the surface of the Earth with a velocity v = v_{e} /2, where v_{e} is the escape velocity. What is the maximum height h reached by the particle in terms of the Earth radius R ?$

A. $R /3$
B. $R /2$
C. $R$
D. $2 R /3$

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Correct answer: A — $R /3$

Solution

Using conservation of energy, 1/2 m (v_{e} /2)^{2} - GM m / R = - GM m / (R + h) . Since v_{e}^{2} = 2 GM / R, we find h = R /3 .

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Solution

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More Gravitation practice questions

$A particle is projected vertically upwards from the surface of the Earth with a velocity v = v_{e} /2, where v_{e} is the escape velocity. What is the maximum height h reached by the particle in terms of the Earth radius R ?$