Escape Speed

What is escape velocity? Obtain an expression for it.

Calculate the escape velocity(in $\mathrm{km} {\mathrm{s}}^{-1}$) in kilometres of a body from the Earth's surface. ($g=9.8 \mathrm{m} {\mathrm{s}}^{-2}, R=6400 \mathrm{km}$)

If the earth were made of wood, its mass would be $10\%$ of its current mass. The escape velocity is $x \mathrm{km} {\mathrm{s}}^{-1}$, if the Earth were made of wood. (Escape velocity of earth is $11.2 \mathrm{km} {\mathrm{s}}^{-1}$) (Write the value of $\left[x\right],$where $\left[ \right]$ is the greatest integer function)

An object projected with a velocity greater than or equal to $11.2 \mathrm{km}/\mathrm{s}$ will not return to earth. Explain reason.

Hydrogen is in abundance around the sun but not around earth. Explain.

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 space ship$=1000 \mathrm{kg};$ mass of the sun$=2\times {10}^{30} \mathrm{kg};$ mass of mars$=6.4\times {10}^{23} \mathrm{kg};$ radius of mars$=3395 \mathrm{km};$ radius of the orbit of mars$=2.28\times {10}^8 \mathrm{km};$ $G=6.67\times {10}^{-11} {\mathrm{Nm}}^2{\mathrm{kg}}^{-2}$.

The escape speed of a projectile on the earth’s surface is $11.2 \mathrm{km} {\mathrm{s}}^{-1}$. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets. (Find the value in kmps upto one decimal place)

Does the escape speed of a body from the earth depend on the mass of the body, the location from where it is projected, the direction of projection, the height of the location from where the body is launched?