Question

let's keep velocity of a body kept at surface of a planet is you is it is projected at a speed of 200% more than the escape speed then its speed is interstellar space will be​

Answer 1

If a body is projected with speed Vi = KVe (k>1), the final intersteller speed is (√k²-1)Ve 

If a body is projected with speed Vi = KVe (k>1), the final intersteller speed is (√k²-1)Ve if Vi = KVe (k<1) directed vertically upward the maximum height from centre of  earth of radius R attained by the body is  r = R /1-K²

If a body is projected with speed Vi = KVe (k>1), the final intersteller speed is (√k²-1)Ve if Vi = KVe (k<1) directed vertically upward the maximum height from centre of  earth of radius R attained by the body is  r = R /1-K²and hence its maximum height from surface of earth is H=  r-R = (R /1-K²) - R

If a body is projected with speed Vi = KVe (k>1), the final intersteller speed is (√k²-1)Ve if Vi = KVe (k<1) directed vertically upward the maximum height from centre of  earth of radius R attained by the body is  r = R /1-K²and hence its maximum height from surface of earth is H=  r-R = (R /1-K²) - R= RK²/1-K²

If a body is projected with speed Vi = KVe (k>1), the final intersteller speed is (√k²-1)Ve if Vi = KVe (k<1) directed vertically upward the maximum height from centre of  earth of radius R attained by the body is  r = R /1-K²and hence its maximum height from surface of earth is H=  r-R = (R /1-K²) - R= RK²/1-K²By this method now velocity is V+2V = 3V

If a body is projected with speed Vi = KVe (k>1), the final intersteller speed is (√k²-1)Ve if Vi = KVe (k<1) directed vertically upward the maximum height from centre of  earth of radius R attained by the body is  r = R /1-K²and hence its maximum height from surface of earth is H=  r-R = (R /1-K²) - R= RK²/1-K²By this method now velocity is V+2V = 3VSo k=3

If a body is projected with speed Vi = KVe (k>1), the final intersteller speed is (√k²-1)Ve if Vi = KVe (k<1) directed vertically upward the maximum height from centre of  earth of radius R attained by the body is  r = R /1-K²and hence its maximum height from surface of earth is H=  r-R = (R /1-K²) - R= RK²/1-K²By this method now velocity is V+2V = 3VSo k=3Finally intersteller  speed = (√k²-1) viz. √8 = 2√2

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