Question

A rocket of mass m is launched vertically from surface of the earth with an initial speed V. Assuming the radius of earth to be R and negligible resistance the maximum height attained by the rocket above the surface of the earth is: 1) R/{gR/2V^2-1} 2)R{gR/2V^2-1} 3)R/{2gR/V^2-1} 4)R{2gR/V^2-1}

Answer 1

this is the answer of your math

Answer 2

answer : option (3) R/(2gR/v² - 1)

A rocket of mass m is launched vertically upwards from the surface of the earth with an initial speed v.

let at maximum height h, velocity of rocket becomes zero. i.e., kinetic energy of body at that point becomes zero.

from conservation of energy Theorem,

initial kinetic energy = potential energy of rocket at the highest point.

⇒1/2 mv² = mgh/(1 + h/R)

⇒1/2 v² = ghR/(R + h)

⇒v²/2 = gh [ R/(R + h)]

⇒v²(R + h) = 2ghR

⇒v²R = (2gR - v²)h

⇒h = v²R/(2gR - v²) = R/(2gR/v² - 1)

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