$A$ particle is projected from the surface of the earth with a velocity equal to twice the escape velocity. When the particle is very far from the earth,its speed would be

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: The kinetic energy needed to project a body of mass $m$ from the Earth's surface to infinity is $\frac{1}{2} mgR$,where $R$ is the radius of the Earth.
Reason $R$: The maximum potential energy of a body is zero when it is projected to infinity from the Earth's surface.
In the light of the above statements,choose the correct answer from the options given below.

$A$ body is projected up with a velocity equal to $\frac{3}{4}$ of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth $= R$)

$A$ rocket is launched straight up from the surface of the earth. When its altitude is $\frac{1}{3}$ of the radius of the earth,its fuel runs out and therefore it coasts. If the rocket has to escape from the gravitational pull of the earth,the minimum velocity with which it should coast is (Escape velocity on the surface of the earth is $11.2 \ km/s$.) (in $km/s$)

$A$ body is projected vertically upwards from the Earth's surface with velocity $2 V_e$,where $V_e$ is the escape velocity from the Earth's surface. The velocity when the body escapes the gravitational pull is

$A$ projectile is projected with velocity $k{v_e}$ in the vertically upward direction from the ground into space. (${v_e}$ is the escape velocity and $k < 1$). If air resistance is considered to be negligible,then the maximum height from the center of the Earth to which it can go will be: ($R$ = radius of Earth)