The escape velocity from Earth is $v_{es}$. $A$ body is projected with a velocity of $2v_{es}$. With what constant velocity will it move in the interplanetary space?

The ratio of the radius of the Earth to that of the Moon is $10$. The ratio of acceleration due to gravity on the Earth and on the Moon is $6$. The ratio of the escape velocity from the Earth's surface to that from the Moon is

$A$ particle is kept at rest at a distance $R$ from the surface of the Earth (of radius $R$). The minimum speed with which it should be projected so that it does not return is

Is it necessary to provide an initial speed of $11.2 \, km/s$ to a rocket launched from Earth?

$A$ mass of $6 \times 10^{24} \ kg$ is to be compressed into a sphere in such a way that the escape velocity from the sphere is $3 \times 10^8 \ m/s$. What should be the radius of the sphere? (Given: $G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$)

$A$ certain object is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half the escape velocity. The maximum height attained by the object will be