The escape velocity from earth is v_(e). A body is projected with velocity 2v_(e). With what constant velocity will it move in the inter planetary space ?

The escape velocity from earth is v_(e). A body is projected with velo

1.	The escape velocity from earth is v_(e). A body is projected with velocity 2v_(e). With what constant velocity will it move in the inter planetary space ?
Answer» `v_(e)` `sqrt(2)v_(e)` `sqrt(3)v_(e)` `sqrt(5)v_(e)` Solution :`U_(i)+K_(i)=U_(f)+K_(f)` `rArr-(GMm)/(R)+(1)/(2)m(2v_(e))^(2)=0+(1)/(2)MV^(2)` or `-(GM)/(R)+2v_(e)^(2)=(1)/(2)V^(2)` or `-(2GM)/(R)+(8GM)/(R)=v^(2)` or `v=sqrt((6GM)/(R))=sqrt(3((2GM)/(R)))=sqrt(3(2gR))=sqrt(3)v_(e)`.