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Grade 11IIT JEE Entrance Exam

the escape speed of a projectile on the earth surface is 11.2 kilometre per second a body is projected out with thrice this speed what is the speed of the body far away from the Earth ignorance of the sun and other planets

Sudhanva G V

7 Years agoGrade 11

1 Answer

Arun

Approved Tutor Answer7 Years ago

Escape velocity of a projectile from the Earth, v_esc= 11.2 km/s
Projection velocity of the projectile, v_p = 3v_esc
Mass of the projectile = m
Velocity of the projectile far away from the Earth = v_f
Total energy of the projectile on the Earth = (1/2)mv_p² – (1/2)mv_esc²
Gravitational potential energy of the projectile far away from the Earth is zero.
Total energy of the projectile far away from the Earth = (1/2)mv_f²
From the law of conservation of energy, we have
(1/2)mv_p² – (1/2)mv_esc² = (1/2)mv_f²
v_f = ( v_p² – v_esc²)^1/2
= [ (3v_esc)² – v_esc² ]^1/2
= √8 v_esc
= √8 × 11.2 = 31.68 km/s.

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