Does the escape speed of a body from the earth depend on
(a) the mass of the body,
(b) the location from where it is projected,
(c) the direction of projection,
(d) the height of the location from where the body is launched?
| Factor | Dependence? | Explanation |
|---|---|---|
| (a) Mass of the body | No | Mass \( m \) cancels out in derivation; \( v_e \) independent of projectile mass. |
| (b) Location from where projected | Yes | Depends on distance \( r \) from Earth's center; varies with latitude slightly due to Earth's shape. |
| (c) Direction of projection | No | Scalar speed for escape; direction affects trajectory but not required speed magnitude. |
| (d) Height of location | Yes | Increased height means larger \( r \), reducing \( v_e \) since \( v_e \propto \frac{1}{\sqrt{r}} \). |