A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. (${v_e}$ is escape velocity and $k < 1)$. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)
A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. (${v_e}$ is escape velocity and $k < 1)$. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)
$\frac{R}{{{k^2} + 1}}$
$\frac{R}{{{k^2} - 1}}$
$\frac{R}{{1 - {k^2}}}$
$\frac{R}{{k + 1}}$
A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. (${v_e}$ is escape velocity and $k < 1)$. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)
Kinetic energy = Potential energy
$\frac{1}{2}m\,{(k{v_e})^2} = \frac{{mgh}}{{1 + \frac{h}{R}}}$==> $\frac{1}{2}m{k^2}2gR = \frac{{mgh}}{{1 + \frac{h}{R}}}$
$ \Rightarrow \,h = \frac{{R{k^2}}}{{1 - {k^2}}}$
Height of Projectile from the earth's surface = h
Height from the centre $r = R + h = R + \frac{{R{k^2}}}{{1 - {k^2}}}$
By solving $r = \frac{R}{{1 - {k^2}}}$
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