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A particle is fired vertically upward from earth’s surface and it goes up to a maximum height of 6400 km. Find the initial speed of particle.

A particle is fired vertically upward from earth’s surface and it goes up to a maximum height of 6400 km. Find the initial speed of particle.

Grade:upto college level

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Sol. The particle attain maximum height = 6400 km. On earth’s surface, its P.E. & K.E. E base e (1/2) mv^2 + (-GMm/R) …(1) In space, its P.E. & K.E. E base s (GMm/R + h) + 0 E base s (-GMm/R + h) …(2) (∴ h = R) Eqating (1) & (2) - GMm/R + 1/2 mv^2 = GMm/2R Or (1/2) mv^2 = GMm (-1/2R + 1/R) Or v^2 = GM/R = 6.67 * 10^-11 * 6 * 10^24/6400 * 10^3 = 40.02 * 10^13/6.4 * 10^6 = 6.2 * 10^7 = 0.62 * 10^8 Or v = √0.62 * 10^8 = 0.79 * 10^4 m/s = 7.9 km/s.

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