Question

A rocket is fired vertically from the surface of the earth with a speed v How far from the earth does the rocket go before returning to the earth ?

(where is the radius of the earth and g is acceleration due to gravity)

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Answer 2

Let the rocket reaches a height h form the surface of earth.

Total energy at the surface of the earth is

Where m and are the masses of rocket and earth respectively.

At highest point, the velocity of the rocket becomes zero.

Total energy at the highest point is

According to law of conservation of energy,

$\therefore \frac { 1 } { 2 } \mathrm { mv } ^ { 2 } - \frac { \mathrm { GM } _ { \mathrm { E } } \mathrm { m } } { \mathrm { R } _ { \mathrm { E } } } = - \frac { \mathrm { GM } _ { \mathrm { E } } \mathrm { m } } { \mathrm { R } _ { \mathrm { E } } + \mathrm { h } }$

$v ^ { 2 } R _ { E } = 2 g R _ { E } h - v ^ { 2 } h$