Question

A rocket is launched to travel vertically upwards with a constant velocity of 20 m/s. After travelling for 35 seconds the rocket develops a snag and its fuel supply is cut off. The rocket then travels like a free body. What is the total height achieved by it ? After what time of its launch will it come back to the earth ?

Solution

Given that,
Upward distance covered by the rocket in first 35 s,
$Using space the space second space equation space of space motion comma space straight s space equals space ut space equals space 20 cross times 35 space equals space 700 space straight m When space the space fuel space is space cut minus off colon straight u space equals space plus 20 space straight m divided by straight s space comma space straight g space equals space minus 10 space straight m divided by straight s squared comma space straight v space equals space 0 Therefore comma space space space space space space space straight v squared space minus space straight u squared space equals space 2 gs space rightwards double arrow space left parenthesis 0 right parenthesis squared space minus space left parenthesis 20 right parenthesis squared space equals space 2 cross times left parenthesis negative 10 right parenthesis cross times straight s rightwards double arrow space straight s space equals space 400 over 20 space equals space 20 space straight m Total space height space achieved space equals space 700 plus 20 space equals space 720 space straight m Also comma space Time comma space straight t space equals space fraction numerator straight v minus straight u over denominator straight g end fraction space equals space fraction numerator 0 minus 20 over denominator negative 10 end fraction minus 2 space straight s For space downward space motion space of space the space rocket comma space straight u space equals space 0 space straight m divided by straight s comma space straight s space equals space minus 720 space straight m comma space straight g space equals space minus 10 space straight m divided by straight s squared Now comma space using space the space second space equation space of space motion comma space minus space 720 space equals space 0 plus 1 half cross times left parenthesis negative 10 right parenthesis straight t squared space space space space space space space space space space straight t squared space equals space 144 straight i. straight e. comma space space straight t space equals space square root of 144 space equals space 12 space sec Total space time space taken space equals space 35 space plus space 2 plus 12 space equals space 49 space sec$

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Atoms And Molecules

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