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Calculate the escape velocity for a part...

Calculate the escape velocity for a particle 1600km above earth's surface. Given `g= 9.8 m//s^(2), R= 6400km`

Text Solution

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We are given: `g= 9.8 m//s^(2), R= 6400km= 6.4 xx 10^(6)m`
`h= 1600km = 1.6 xx 10^(6)m`
`R+h= (6.4+1.6) xx 10^(6)= 8 xx 10^(6)m`
We are to calculate, escape velocity of particle at 1600km above earth.s surface. Using relation
`V_(e)= sqrt(2g_(h) (R+h))`. Also `g_(h)= (gR^(2))/((R+h)^(2))`
`V_(e)= sqrt((2 xx gR^(2))/((R+h)^(2)) xx (R+h)) =sqrt((2gR^(2))/(R+h))`
`therefore V_(e)= sqrt((2 xx 9.8 xx (6.4 xx 10^(6))^(2))/(8 xx 10^(6)))=10.02 xx 10^(3) m//s`
`V_(e)= 10.02 km//s`
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