$A$ 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

The escape velocity for a body projected vertically upwards from the surface of earth is $11.2 \ km/s$. If the body is projected at an angle of $45^o$ with the vertical,the escape velocity will be ......... $km/s$.

$A$ spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the spaceship $= 1000 \; kg$,mass of the Sun $= 2 \times 10^{30} \; kg$,mass of Mars $= 6.4 \times 10^{23} \; kg$,radius of Mars $= 3395 \; km$,radius of the orbit of Mars $= 2.28 \times 10^{8} \; km$,$G = 6.67 \times 10^{-11} \; N m^{2} kg^{-2}$.

$A$ space station is at a height equal to the radius of the Earth. If $V_{E}$ is the escape velocity on the surface of the Earth,the escape velocity on the space station is __ times $V_{E}$.

$A$ rocket is launched straight up from the surface of the earth. When its altitude is one-fourth of the radius of the earth,its fuel runs out and it coasts. What is the minimum velocity the rocket must have when it starts to coast if it is to escape from the gravitational pull of the earth? (Escape velocity on the surface of the earth is $11.2 \ km/s$)

$A$ rocket is fired vertically with a speed of $4 \ km/s$ from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth (in $km$)? (Take radius of Earth $R = 6.4 \times 10^6 \ m$ and $g = 10 \ m/s^2$)