﻿ A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1. If 20% of its initial energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars = 6.4× 1023 kg; radius of mars = 3395 km; G = 6.67× 10-11 N m2 kg–2. from Physics Gravitation Class 11 Manipur Board

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A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1. If 20% of its initial energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars = 6.4× 1023 kg; radius of mars = 3395 km; G = 6.67× 10-11 N m2 kg–2.

Initial velocity of the rocket, v = 2 km/s = 2 × 103 m/s

Mass of Mars, M = 6.4 × 1023 kg

Radius of Mars, R = 3395 km = 3.395 × 106 m

Universal gravitational constant, G = 6.67× 10–11 N m2 kg–2

Mass of the rocket =

Initial kinetic energy of the rocket = mv

Initial potential energy of the rocket =

Total initial energy = mv2 -

If 20 % of initial kinetic energy is lost due to Martian atmospheric resistance, then only 80 % of its kinetic energy helps in reaching a height.

Total initial energy available =
= (80/100) × (1/2) mv2 -

=  0.4mv2 -

Maximum height reached by the rocket =

At this height, the velocity and hence, the kinetic energy of the rocket will become zero.

Total energy of the rocket at height h =

Applying the law of conservation of energy for the rocket,

0.4mv2 -   =

0.4v2 =

=

=

h =

=

=

=

=

= 495 × 103 m

= 495 km.
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